Scientific Inquiry

"Scientific inquiry, in sum, is the pursuit of mechanistic, coherent accounts of natural phenomena." - from Seeing the Science in Children's Thinking: Case Studies of Student Inquiry in Physical Science

NY Times on Math Ed

Apparently not everyone agrees that mathematics education research is the gold standard. In the NY Times today, there was an article on parents and mathematics professors rebelling against "fuzzy" math.

“The Seattle level of concern about math may be unusual, but there’s now an enormous amount of discomfort about fuzzy math on the East Coast, in Maine, Massachusetts and Pennsylvania, and now New Jersey is starting to make noise,” said R. James Milgram, a math professor at Stanford University. “There’s increasing understanding that the math situation in the United States is a complete disaster.”

Who is James Milgram? What research has he conducted in how people learn? This leads me to their website, refuting several of the NCTM standards, by citing 3 peer-reviewed studies (and numerous other opinion articles). There are thousands of papers written in mathematics education, so three studies does not make a case. (In particular Klahr and Nigam.)

It seems so strange to me who is "allowed" to criticize education, teachers, curriculum, and standards. Does succeeding at math make you an expert on how people learn math, or how to best teach math? Anyone who has taken a university mathematics course surely can answer that question with a "no."

This is not to say that learning the "basics" is a meaningless endeavor or should not be part of the standards (though I can't tell you the last time I did long division, and I use problem solving strategies daily). I just think the research is ongoing, we don't know the answer yet, and anyone who claims differently has a limited view of what it is to have learned math.

One interesting point that this article does raise is a parent quoting a teacher who notes: "We don’t teach long division; it stifles their creativity." The disconnect between the intent of curriculum and the perceived intent by teachers is worrisome.

What do we know about mathematics curricula?

Thinking about where mathematics education is, what science education can learn from them, and how science differs from math, has been intriguing to me lately. I rely on certain core ideas in reasoning about new problems in science: energy, momentum, certain conservation laws, symmetries-- and it seems to me that there are some key "content" ideas that can help anchor your science thinking. I wonder if this is different from mathematics.

Schoenfeld, describing a mathematics course in problem solving that is not tied to a particular "content" topic but rather to problem solving heuristics, quotes a conversation with the department chair. He's trying to get credit towards the major for students who take the course, and argues that students in this class can outperform senior math majors on difficult math problems. The department chair replies: "I'm sure you're right, but we still can't give credit toward the major. You're not teaching them content-- you're just teaching them to think."

Schoenfeld goes on to say (p. 4):

The moral of this story and the reason that I tell it is that it demonstrates clearly that what counts as mathematical content depends on one's point of view. From Professor Y (the dept. chair)'s perspective, teh mathematical content of a course is teh sum total of the topics covered...

I would characterize the mathematics a person understands by describing what that person can do mathematically, rather than by an inventory of what a person "knows."... Note that this performance standard is the one that Professor Y lives by in his professional life, and the one that he uses to judge his colleagues.

This course he describes feels similar to a science course I've co-taught, where the students brought in questions and then reasoned through them. Topics included "will a human blow up in space (or freeze)" and "why is the sky blue." But in these courses I didn't just provide guidance on heuristics or scientific thinking, but also added a lot of content-- about how things lose heat, how prisms work, etc. And while some students might be well-prepared to reason scientifically at the end of the course, I doubt they could go toe-to-toe with a student with more content knowledge.


from Schoenfeld, A.H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55 - 80.

Towards an agreement on the goals of science instruction?

At a conference here at LessonLab on the use of video in teacher education, I was struck by the lack of consensus on what we should be teaching in science, what good instruction looks like, what we're asking teachers to do and why. I kept thinking that the findings of others' studies can scarcely inform my research because I'm interested in very different ways of speaking, talking, and doing science.

Mathematics education, I frequently hear, is much "farther along." And the few presentations and papers I've read from math ed convince me that this is true. But is science ed even having the necessary conversations to become "farther along"?

Reading Schoenfeld's "Purposes and Methods of Research in Mathematics Education" and "The Math Wars" now provides some interesting background on what mathematics education research is all about.

He notes that there are two main purposes, on pure and one applied:

- Pure (basic science): To understand the nature of mathematical thinking, teaching and learning;
- Applied (engineering): To use such understandings to imporve mathematics instruction.

Simply put, the most typical educational questions asked by mathematicians-- 'what works' and 'which approach is better?'-- tend to be unanswerable in principle. The reason is that what a person will think works will depend on what that person values... Just what do you want to achieve? What understandings, for what students, under what conditions, with what constraints?

The appropriate way to proceed was to look at the curriculum, identifying important topics and specifying what it means to have a conceptual understsanding of them. ... As a result of extended discussions, the NSF effort evolved from one that focused on documenting the effects of calculus reform to one that focused on developing a framework for looking at the effects of calculus instruction.

Looking at the evolution of the mathematics standards and the spirit behind this document, I wonder if science education was too quick to replicate math's success and create its own standards?

As Bruner said:

To instruct someone... is not a matter of getting him to commit results to mind. Rather, it is to teach him to participate in the process that makes possible the establishment of knowledge. We teach a subject not to produce little living libraries on that subject, but rather to get a student to think mathematically for himself, to consider matters as an historian does, to take part in the process of knowledge-getting. Knowing is a process not a product. (1966: 72)

How do the science standards support this view of instruction and knowing?

"Schools as Knowledge Building Organizations"

Scardamalia has noted that educators tend to think students need to know all the facts and findings of a discipline before they can start building knowledge in that field. So, for example, first students must know what atoms are, what protons and electrons are, must know about the distribution of charges and how things attract and repel, what a metallic bond is versus a covalent bond, must be told all of these facts, before they can begin to build knowledge about, say, conductors and insulators. Taking issue with this, she notes:

"...What makes work 'scientific' is a matter of continuing controversy and is not a matter to be settled here; but we may at least agree that science is a form of social practice that goes on, with wide variations, in groups recognized as scientific...We see school-age students as ... having about 500 years of science to catch up on... They can begin functioning as real scientists as soon as they are able to engage in a form of social practice that is authentically scientific, one that is concerned with the solution of recognizably scientific problems in recognizably scientific ways."

from Scardamlia, M. and Bereiter, C. (1999). In D. Keating and C. Hertzman (Eds.), Today's Children, tomorrow's society: The developmental health and wealth of nations. New York: Guilford.

SPARC Author Addendum

When you publish research, consider using a version of the SPARC author addendum. Many universities are now encouraging it.

APA Learner-Centered Psychological Principles

From the American Psychological Association, a collection/distillation of ed psych type findings on principles for learning. The document began when GHW Bush was pushing for more accountability in education and members of the APA began wondering:

How can we bring to the attention of the public, educators and policy makers what we know about learning [and] what we know about motivation that can influence some of these decisions that may be well intended but certainly weren’t going in a direction that many of us felt as people who understood learning and motivation would be for the good of children? (from McCombs at ICLS).

These principles are deliberately not discipline-specific. But they're interesting-- and the wording ("successful learners do X", rather than "successful learning environments have Y") is worth thinking about. As is the first point, "The learning of complex subject matter...".-- I think that understanding complex subject matter is an outcome of "active, goal-directed, and self-regulated" engagement with ideas. When we focus exclusively on learning as "learning complex subject matter" -- instead of learning as adopting certain habits of mind/appropriating tools of disciplines (in particular discursive practices)-- we can't help but fall back into assessments that assess whether or not students "know" complex subject matter.

Clark and Shaefer

Clark and Shaefer's 1989 paper on grounding.

I've been looking into the role that analogies play in scientific discourse-- trying to distinguish the interactive, dialogic role of analogies from the more cognitive, logical problem-solving role that characterizes much of the research on analogical reasoning.

Clark and Shaefer's work on grounding in discourse is a possible direction for understanding analogies:

When people take part in a conversation, they bring with them a certain amount of baggage— prior beliefs, assumptions and other information. Part of that baggage is their common ground, which Stalnaker (1978) described this way: “roughly speaking, the presuppositions whose truth he takes for granted as part of the background of the conversation… Presuppositions are what is taken by the speaker to be the common ground of the participants in the conversation, what is treated as their common knowledge or mutual knowledge.” (p. 320, original emphases)… in actual conversations, the presuppositions vary from one participant to the next, though usually not too drastically. (p 260 of C & S)

Analogies can perhaps be understood as a move to establish common ground-- choosing a domain in which the participants can agree on all the presuppositions regarding the structure of the domain and the kinds of ontologies involved. Of course, the participants might disagree on the appropriateness of the analogy (might be a kind of structure-mapping move as this happens). Most of the analogies in my corpus (of spontaneously generated analogies in science discourse) are not used to map but to ground.-- Once the analogy is agreed on as appropriate, it has served its purpose and is no longer used.

From the 2006 ICLS

Major talks from the 2006 International Conference of the Learning Sciences are available online.

Some highlights and quotes from "The Learning Sciences and the Future of Education:"

from Allan Collins: "Education is seeping out of schools"-- we're moving from "just in case" education to "just in time" education.

from Jere Confrey: "It's not just knowing but letting know."

from Janet Kolodner: "Learning is not just about content: it needs to focus on 'becoming'—helping people to grow in capabilities and awareness and disposition (which includes learing content)."

from Marlene Scardamalia: "What would an education look like where we actually thought about innovation from the beginning with learning as a by-product of continual and creative work with ideas?"

How would we define a discipline- a physics class, say- if the content is a by-product of engagement with ideas? Would it have to focus on discipline-specific ways of asking and answering rather than the topic of investigation?

Following their talks, some ideas in the following conversations:

Allan Collins: "The Learning Sciences and NSF have spent a lot of money to invest in developing curricula and learning environments. At the same time we’ve seen this huge increase on accountability, and the testing methodology is tied to every kid learning the same things at the same time and it’s fundamentally incompatible with the kinds of power that the learning environments we’ve been developing enable. We want kids to pursue things deeply that they care about. And the technologies make that possible- you can break the lock-step schooling with these powerful technology environments. But if the tests we’re using to evaluate kids depend on a lock-step system, then all the technology we build is going to go nowhere.

The second thing I want to say is: that’s one deep incompatibility between what real school as we understand it is and what technology empowers. Technology empowers kids taking control of their education. It empowers learning what you’re most- I mean, this personalization this customization it lets kids learn what’s important to them. And if we ignore the imparities (?) of technology as we design education systems, we’re not going to go anywhere. So I think we’re going to need to understand what technology does well and understand that that’s incompatible with the ways that people understand what schools do. And because of that incompatibility a lot of education is going to be taking place outside of schools. And so we need to begin to think about how we can use the affordances of technology and the changing environment to make our educational systems work in new venues."

It seems to me that this goes far beyond technology. Authentic scientific discourse, inquiry, discovery teaching-- all empower these same things that Collins claims to be a strength of technology. I'd rather see schools change to match our understanding of what education can be than see our educational technologies and experiences taken out of schools.

This resonates with findings from a RAND study on the effectiveness of reform science instruction: "It is also important to note the influence of high-stakes accountability testing on teaching practices. Teachers reported that the testing environment influenced their use of reform-oriented practices despite the training they had received. In particular, many teachers believed that the reform-oriented practices were likely to be less effective than other kinds of practices for promoting high scores on state accountability tests. Future research on the effectiveness of reform-oriented instruction needs to recognize that instructional reforms are not carried out in a vacuum, and it should examine the broader contextual factors as well as the specific elements of the intervention." (p. xviii - xix)

It also suggests that having specific content goals in a classroom is necessarily inconsistent with reform instruction.

From Jere Confrey, in response to a question on diagnostic, as opposed to traditional high stakes testing:

"Three things that go into courts- and I read a number of the court cases- the three things that they talk about in testing are: reliability, validity, fairness. The only thing that ends up (practically) in the courtroom is reliability because it has a formula attached therefore it can be disputed....We don’t debate in the courts issues of validity and we have very poor understanding how to talk about fairness with regard to legal and court practices. Sure let’s have these other methods [low-stakes/diagnostic tests]. But the high stakes tests have got to be a target for us because it’s driving so much of what’s happening in the schools and we have to go after- from the perspective of our field- what it means to define and measure and take to the court-level issues of validity and issues of fairness in a way that will drive the system in directions we’re comfortable with."

A question is asked about the structure of the discipline being lost in "just in time" education.

Allan Collins: "My general argument is: I am not an advocate for what is happening. I’m not saying we’re moving towards a halcyon environment with this revolution. Downsides also relate to equity, citizenship, and you make one I hadn’t thought about previously. That’s a serious problem. Now it is the case that as you learn in a workplace or an adult education center, you may in fact go deeply into some subject area, such as the history of the American nation. And you may get an understanding of the structure of that discipline. But as we’re designing an environment we need to think about this issue of the structure of knowledge and we need to understand that those environments...we need to be thinking how to make this transition because it’s happening. We need to think seriously from a broad educational system point of view how to make that transition."

Upcoming elections

You spend a lot of tax money on research, shouldn't you listen to the results? Support the role of scientific research in informing policy; see here.

Science Thinking Blog

Science Education, Education Science, Learning Science, and Science Learning were all taken. As was Talking Science. So "Science Thinking" blog is actually more about learning science. Posts to follow.