Teacher Pay on Oregon Ballot

Most policy issues are too complicated to warrant direct democracy. That's why -- like 'em or hate 'em -- we elect presidents, governors, legislators, school board members, and the like to do that detailed work. The general public, by and large, doesn't have the time (or interest?) to wade into these issues at a level of depth that they require. Such is the case with teacher pay, especially when the issue is how it can fairly and accurately be tied to student outcomes. That's complicated stuff.

Oregon begs to differ. Oregon allows such complex issues to be voted on by direct public referendum. In fact, it leads the nation in such "voter" initiatives. Now, Oregon is one of my favorite places, but on this issue, I just think it is dead wrong.

The Associated Press reports that Oregon's 2008 ballot will feature 12 measures in all, one of which would require that teachers be paid based on "classroom performance" rather than on experience or seniority. It is sponsored by an unsuccessful Republican gubernatorial candidate and founder of Oregon Taxpayers United.

Oregon voters rejected a similar ballot measure eight years ago.

Hey, I'm all for thinking big and bold about how to change teacher compensation (see here, here, and here), but this ain't the way to do it.

And lest you think that ballot initiatives take the money out of politics, check out who is funding them in Oregon in 2008. For more information about Oregon's history of ballot measures, check out this handy guide from the Ballot Initiative Strategy Center.

Finally, a VC with a good academic record

Got this piece of news from a friend from one of the public unis. Zaini Ujang, at 43, is the youngest VC in a public university, in this case, UTM. Unlike the UITM VC, Prof Zaini Ujang is a legit academic with a history of academic publications in peer reviewed journals. And he doesn't boast that he's a life long UMNO member and is proud of his publication record. You can view his publication record here. It's this kind of appointment which gives me some hope in the public university system in Malaysia. Another sign that UTM is moving in the right direction? I recently got to know two Malaysian PhD students in Cambridge who are sponsored by UTM. If they and others like them go back to UTM, it's a good sign for that institution.

More On The Generational Divide in Teaching

The generational divide in the teaching profession that I discussed back in August ('A Generational Divide Over Teacher Pay') is expounded upon by Paul Tough on his Schoolhouse Rock blog on slate.com.

10 remarkable female mathematicians

The Math-Blog presents a nice overview of some of the greatest female mathematicians ever. No doubt, most of the mathematicians we ever hear of are men, but there still are several female mathematicians that have made significant contributions to the field. Here is part of the introduction to this list of mini-biographies:

These women were often groundbreakers, highly determined and very dedicated. They are shining examples of the fact that mathematics is not a “boys only” club, even if at many points in time it’s appeared that way on the surface. Today their work is recognized and appreciated, and they stand as fantastic sources of inspiration for a new generation of students and math enthusiasts – both female and male.

10 remarkable female mathematicians

The Math-Blog presents a nice overview of some of the greatest female mathematicians ever. No doubt, most of the mathematicians we ever hear of are men, but there still are several female mathematicians that have made significant contributions to the field. Here is part of the introduction to this list of mini-biographies:

These women were often groundbreakers, highly determined and very dedicated. They are shining examples of the fact that mathematics is not a “boys only” club, even if at many points in time it’s appeared that way on the surface. Today their work is recognized and appreciated, and they stand as fantastic sources of inspiration for a new generation of students and math enthusiasts – both female and male.

The Community Agenda for Schools

In fairness, apparently The Community Agenda for America's Public Schools is the other major reform agenda that has recently emerged (along with the Broader, Bolder group discussed in the last post).

At the core of the Community Agenda are a set of recommendations for collaborations between schools and "the community":

This idea—fully embraced—would make all Americans responsible and accountable for excellent schools and the positive development of all our young people. Every institution that influences positive outcomes for children and youth must be part of the agenda—schools, families, government, youth development organizations, health, mental health and family support agencies, higher education and faith-based institutions, community organizing and community development groups, unions, and business. Each brings assets and expertise; each must change how it does its work; and all must work together to close the opportunity gap

The recommendations (listed below in edited form) mostly, but not entirely, seem to define "community" as "institutions that serve the community."  One problem with this definition is that these institutions are generally led by people who don't come from or live in impoverished communities.  Nonetheless, it would be nice if local institutions worked better together.  The idea of "one stop shops" for services, and school based services--especially health services--seems important.

But this seems to assume that these institutions haven't already been trying to work together to one extent or another.  Whether we like it or not, the fact is that in impoverished urban areas, at least, schools, as institutions, tend not to work and play well with others for a whole range of reasons.  It is difficult to mandate "community participation" for schools just as it is difficult to mandate "better pedagogy."  These relationships are complex, context-bound, and often personality driven.  Many if not most "collaborations" between schools and communities actually involve local agencies using school space for after school programs, for example, but not really having that much substantively to do with the actual institution of the school.  It's not clear to me that urging schools to engage more with the community will end up having much more overall effect than efforts to urge teachers to teach better.  

There are examples of effective inter-agency collaboration, as the group's call to action notes.  But can these be broadly and widely replicated with any speed in any effective way?  I'm not sure, and it's certainly not where I'd put my marbles if I had any.  (But see Schorr's book for the best discussion of the challenges of replication that I now of.  It actually discusses one of the community collaborations noted in the Community Agenda statement.  Anyone out there know of more recent work?)

Furthermore, the recommendation for more effective "involvement" between schools and communities more broadly seems pretty "pie in the sky."  In a review of the literature around community-school relationships, I could find NO example of a broad based, replicable model for fostering this kind of involvement.  Schools as institutions are almost completely uninterested in opening themselves up to real engagement by people and groups who are actually located IN impoverished communities (at least in the urban literature I looked at).  I have talked to some people who were grumpy about this finding--but aside from anecdotal stories, no one has actually presented a coherent argument to me about why I am wrong.  (I'd love to be wrong--but I doubt I am).  The point isn't that schools can't do better--see Joyce L. Epstein's work, for example.  The point is that what they do seem to be able to do doesn't seem likely to produce robust shifts in community participation understood in the broadest sense.  Without "authentic" participation by any definition, this could easily become a project designed to teach those poor parents how to raise their kids.  

I did find that engagements between schools and independent groups designed to enhance community empowerment (among others) did sometimes seem to be effective.  And the plan does mention community organizing groups among others.  But except in rare cases, community organizing groups simply do not have the current capacity to engage with a broad range of school in our cities.  Many can barely stay alive in the first place.  One would have to imagine how significant resources could be put into these organizing groups--$ that does not flow through the schools who have little pragmatic interest in reducing their own control.  It's hard to imagine how this would happen.  And there is little in the recommendations that gives me hope that the groups 

Given this, the differences between this model and the Broader, Bolder model seem limited to the Community Agenda's focus on community relationships as the central tool, and on a more limited focus on the importance of non-school issues on student achievement in the Community Agenda model.  The problem with this focus on community is that it could easily draw emphasis away from the need for services and resources, which is vastly more needed than the coordination of these services (which mostly don't exist), although coordination would be wonderful.  In fact, there seems to me to be something of a disconnect between their Strategies That Work list, and the Policy Recommendations that follow these (listed below).

Further, there is less acknowledgement here, than in the Broader, Bolder plan that non-school resources are clearly the most important and effective place to intervene if we really want to make an impact on achievement and on the flourishing of children more broadly.  Talk about community collaboration is cheaper than actually finding the kinds of resources discussed by the Broader, Bolder folks.  Ironically, this is why people talk so much about schools as a solution to poverty--because education is cheaper than efforts to actually solve poverty, because talk about education is pretty non-political, and because talk, by itself, without actually doing much for schools is even cheaper.  

So I'm much more drawn to the Broader, Bolder vision than the Community Agenda vision.  The Broader, Bolder folks seem to be addressing the core challenges of education, the challenges that we most need to address, even though it will inevitably be more difficult to actually make change in these areas.

That's my initial response.  What do others think?

The Community Agenda's "Policy Recommendations":

• Results-focused Partnerships

Through results-focused partnerships, the resources of all government and community institutions can be aligned and applied in a more coordinated and effective fashion.

• Youth, Parent, School, and Community Involvement

The people and places affected by public policy must have a voice in its implementation.  We propose that policy be developed to enable youth, parents, and community leaders as well as school leaders, including principals and teachers, to be partners in the planning and oversight of school reform and community initiatives.

• Community-School Coordination

Effective coordination is essential at the school site.  Research shows that students can and will achieve when resources to address their academic and other needs are tailored, coordinated, and accessible.  We recommend policies that provide staff in every school who will coordinate results-focused partnerships, integrate school and community resources based on individual student needs, and engage parents as well as other community members.

• A Broad-Based Accountability Framework

A single standardized test should not be the only basis for judging schools or students.

• Public Access to Data

• Professional Development and Capacity-Building

• Increased Investments

The Community Agenda for Schools

In fairness, apparently The Community Agenda for America's Public Schools is the other major reform agenda that has recently emerged (along with the Broader, Bolder group discussed in the last post).

At the core of the Community Agenda are a set of recommendations for collaborations between schools and "the community":

This idea—fully embraced—would make all Americans responsible and accountable for excellent schools and the positive development of all our young people. Every institution that influences positive outcomes for children and youth must be part of the agenda—schools, families, government, youth development organizations, health, mental health and family support agencies, higher education and faith-based institutions, community organizing and community development groups, unions, and business. Each brings assets and expertise; each must change how it does its work; and all must work together to close the opportunity gap

The recommendations (listed below in edited form) mostly, but not entirely, seem to define "community" as "institutions that serve the community."  One problem with this definition is that these institutions are generally led by people who don't come from or live in impoverished communities.  Nonetheless, it would be nice if local institutions worked better together.  The idea of "one stop shops" for services, and school based services--especially health services--seems important.

But this seems to assume that these institutions haven't already been trying to work together to one extent or another.  Whether we like it or not, the fact is that in impoverished urban areas, at least, schools, as institutions, tend not to work and play well with others for a whole range of reasons.  It is difficult to mandate "community participation" for schools just as it is difficult to mandate "better pedagogy."  These relationships are complex, context-bound, and often personality driven.  Many if not most "collaborations" between schools and communities actually involve local agencies using school space for after school programs, for example, but not really having that much substantively to do with the actual institution of the school.  It's not clear to me that urging schools to engage more with the community will end up having much more overall effect than efforts to urge teachers to teach better.  

There are examples of effective inter-agency collaboration, as the group's call to action notes.  But can these be broadly and widely replicated with any speed in any effective way?  I'm not sure, and it's certainly not where I'd put my marbles if I had any.  (But see Schorr's book for the best discussion of the challenges of replication that I now of.  It actually discusses one of the community collaborations noted in the Community Agenda statement.  Anyone out there know of more recent work?)

Furthermore, the recommendation for more effective "involvement" between schools and communities more broadly seems pretty "pie in the sky."  In a review of the literature around community-school relationships, I could find NO example of a broad based, replicable model for fostering this kind of involvement.  Schools as institutions are almost completely uninterested in opening themselves up to real engagement by people and groups who are actually located IN impoverished communities (at least in the urban literature I looked at).  I have talked to some people who were grumpy about this finding--but aside from anecdotal stories, no one has actually presented a coherent argument to me about why I am wrong.  (I'd love to be wrong--but I doubt I am).  The point isn't that schools can't do better--see Joyce L. Epstein's work, for example.  The point is that what they do seem to be able to do doesn't seem likely to produce robust shifts in community participation understood in the broadest sense.  Without "authentic" participation by any definition, this could easily become a project designed to teach those poor parents how to raise their kids.  

I did find that engagements between schools and independent groups designed to enhance community empowerment (among others) did sometimes seem to be effective.  And the plan does mention community organizing groups among others.  But except in rare cases, community organizing groups simply do not have the current capacity to engage with a broad range of school in our cities.  Many can barely stay alive in the first place.  One would have to imagine how significant resources could be put into these organizing groups--$ that does not flow through the schools who have little pragmatic interest in reducing their own control.  It's hard to imagine how this would happen.  And there is little in the recommendations that gives me hope that the groups 

Given this, the differences between this model and the Broader, Bolder model seem limited to the Community Agenda's focus on community relationships as the central tool, and on a more limited focus on the importance of non-school issues on student achievement in the Community Agenda model.  The problem with this focus on community is that it could easily draw emphasis away from the need for services and resources, which is vastly more needed than the coordination of these services (which mostly don't exist), although coordination would be wonderful.  In fact, there seems to me to be something of a disconnect between their Strategies That Work list, and the Policy Recommendations that follow these (listed below).

Further, there is less acknowledgement here, than in the Broader, Bolder plan that non-school resources are clearly the most important and effective place to intervene if we really want to make an impact on achievement and on the flourishing of children more broadly.  Talk about community collaboration is cheaper than actually finding the kinds of resources discussed by the Broader, Bolder folks.  Ironically, this is why people talk so much about schools as a solution to poverty--because education is cheaper than efforts to actually solve poverty, because talk about education is pretty non-political, and because talk, by itself, without actually doing much for schools is even cheaper.  

So I'm much more drawn to the Broader, Bolder vision than the Community Agenda vision.  The Broader, Bolder folks seem to be addressing the core challenges of education, the challenges that we most need to address, even though it will inevitably be more difficult to actually make change in these areas.

That's my initial response.  What do others think?

The Community Agenda's "Policy Recommendations":

• Results-focused Partnerships

Through results-focused partnerships, the resources of all government and community institutions can be aligned and applied in a more coordinated and effective fashion.

• Youth, Parent, School, and Community Involvement

The people and places affected by public policy must have a voice in its implementation.  We propose that policy be developed to enable youth, parents, and community leaders as well as school leaders, including principals and teachers, to be partners in the planning and oversight of school reform and community initiatives.

• Community-School Coordination

Effective coordination is essential at the school site.  Research shows that students can and will achieve when resources to address their academic and other needs are tailored, coordinated, and accessible.  We recommend policies that provide staff in every school who will coordinate results-focused partnerships, integrate school and community resources based on individual student needs, and engage parents as well as other community members.

• A Broad-Based Accountability Framework

A single standardized test should not be the only basis for judging schools or students.

• Public Access to Data

• Professional Development and Capacity-Building

• Increased Investments

The work of teaching and the challenge for teacher education

Here is a very interesting presentation held by Deborah L. Ball on a visit to Vanderbilt University. Ball has been in charge of several major projects concerning the teachers' knowledge of mathematics, e.g. the LMT (Learning Mathematics for Teaching) project, and she was also a member of the National Mathematics Advisory Panel, which delivered an important report earlier this year. (See one of my previous posts about this!)

The work of teaching and the challenge for teacher education

Here is a very interesting presentation held by Deborah L. Ball on a visit to Vanderbilt University. Ball has been in charge of several major projects concerning the teachers' knowledge of mathematics, e.g. the LMT (Learning Mathematics for Teaching) project, and she was also a member of the National Mathematics Advisory Panel, which delivered an important report earlier this year. (See one of my previous posts about this!)

Should We Postpone The Election, Too?

UPDATE: It appears that there will be a Obama-McCain tonight. Hold that chicken suit.

-------------------------------------

It looks like it might be time to bring out a guy in a chicken suit for Obama to debate (perhaps Letterman can assist?) as McCain is likely to back out of tomorrow night's presidential debate -- despite this agreement -- due to the lack of agreement on Capitol Hill over the government bailout of rich guys. Makes sense, right? The economy is in the tank, so let's limit the exercise of American democracy. Sounds like a plan written by the Bush Administration, maybe even Uncle Dick himself.

Perhaps we should postpone the election, too. After all, high school civics instructs us that Article II 0f the U.S. Constitution gives Congress the power to set the date of the presidential election. So it's not too late!!! Given the fact that McCain's presence in Washington, DC is so critical the future of the American economy, let's give W another year at the helm and try this whole election thing again in 2009. Maybe that will even give McCain time to reconsider his choice for veep.

I feel an omnibus bill coming on: Wall Street bailout, election postponement. What else?

School Vouchers Are No Silver Bullet

Here is a compelling article by the American Enterprise Institute's Rick Hess about school choice in light of Milwaukee's experience with vouchers over the last two decades. His analysis is not as rosy as you might initially expect from a center/right researcher. But he does continue to see the potential in market-based reforms as long as they are envisioned more expansively and are accompanied with a focus on program growth, provider quality, professionalism, innovation, and accountability.

Many of Hess's proposed elements are exactly the kinds of reform that the Milwaukee voucher community fought tooth and nail over the years -- a fight led by politicized organizations such as School Choice Wisconsin, the Alliance for School Choice, and Advocates for School Choice. All of these organizations are interconnected and are bankrolled by national right-wing foundations, including Milwaukee's own Bradley Foundation. These groups have seemed to care little about the quality of education provided to Milwaukee's largely low-income and minority students -- but have willingly used these kids as political props at pro-voucher rallies during the school day -- and have made their sole focus the preservation of an unregulated and unfettered school voucher system in the city of Milwaukee. That changed a little bit a few years ago when media stories about graft, incompetence, and the utter absence of teaching and learning emerged at a number of Milwaukee voucher schools.

As education policy advisor to Wisconsin Governor Jim Doyle from 2004 to 2006, I was involved in some of these skirmishes with the voucher leadership. Doyle was always clearly on the side of public education and generally steered a wise course through choppy political waters on this issue. However, I continue to believe that a 2006 compromise [2005 Wisconsin Act 125 summary] that injected some of the first ever accountability and quality control into Milwaukee's voucher program still gave away too much. As examples, I'd offer up the evaluation currently being conducted by the privately-funded, voucher-friendly School Choice Demonstration Project, the trouble that state officials are having in getting data from that entity, and the lack of a requirement that voucher schools (funded with more than $100 million in state monies) administer a standardized assessment that would provide parents, policymakers and researchers with comparable student achievement data.

Hopefully, moving forward, all involved will take some of Hess's recommendations under advisement. For now, the Milwaukee voucher program lives on in its current form.

Here are a few excerpts from Hess's article:

Nearly two decades have passed since the enactment of the landmark Milwaukee Parental Choice Program by the Wisconsin legislature. The program and its many supporters had hoped this experiment in school choice would lead the way in transforming American schools. But it is by now clear that aggressive reforms to bring market principles to American education have failed to live up to their billing.
...
Today, the Milwaukee voucher program enrolls nearly 20,000 students in more than 100 schools, yet this growing marketplace has yielded little innovation or excellence. The Milwaukee Journal Sentinel recently described 10 percent of voucher schools as having “alarming deficiencies.” These include Alex’s Academics of Excellence, which was launched by a convicted rapist, and the Mandella School of Science and Math, whose director overreported its voucher enrollment and used the funds to purchase two Mercedes. Veteran Journal Sentinel writer Alan Borsuk has opined, “[Milwaukee Parental Choice Program] has preserved the status quo in terms of schooling options in the city more than it has offered a range of new, innovative, or distinctive schools.”
...
We should have no difficulty conceding Milwaukee’s disappointing record while remaining coolly confident that sensible K–12 market reforms have the potential to boost productivity, spur purposive innovation, provide more nuanced accountability, and make the sector a magnet for talent. Failures to dates should not be read as indictments of market reform but of the notion that “parental choice” programs represent a coherent approach to improving our schools. Reaching that goal will require approaching educational deregulation with an agenda much broader than simply increasing parental choice.
...
The lessons are increasingly clear. If school choice is to enjoy a brighter future than wave upon wave of supposed school reforms past, it is time for reformers to fight not just for choice but for good choices.

Reversibility of thought

Ajay Ramful and John Olive wrote an article entitled Reversibility of thought: An instance in multiplicative tasks, which was published online in The Journal of Mathematical Behavior yesterday. Here is the abstract of the article:

In line with current efforts to understand the piece-by-piece structure and articulation of children’s mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data collected through clinical interviews depict the precise strategies that the participants used to work back to find the missing values in an inverse proportional task. This study also illustrates how a conceptual template generated by one of the participants afforded him considerable flexibility in the multiplicative task. Another outcome of the study is that it shows how the numerical characteristics of the parameters in the problem affected the students’ ability to reverse their thought processes. We infer that there is a need for further research on how students might represent their reversibility schemes in the form of algebraic equations.

Reversibility of thought

Ajay Ramful and John Olive wrote an article entitled Reversibility of thought: An instance in multiplicative tasks, which was published online in The Journal of Mathematical Behavior yesterday. Here is the abstract of the article:

In line with current efforts to understand the piece-by-piece structure and articulation of children’s mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data collected through clinical interviews depict the precise strategies that the participants used to work back to find the missing values in an inverse proportional task. This study also illustrates how a conceptual template generated by one of the participants afforded him considerable flexibility in the multiplicative task. Another outcome of the study is that it shows how the numerical characteristics of the parameters in the problem affected the students’ ability to reverse their thought processes. We infer that there is a need for further research on how students might represent their reversibility schemes in the form of algebraic equations.

Learning about infinity

Florence M. Singer and Cristian Voica wrote an interesting article that was recently published in The Journal of Mathematical Behaviour: Between perception and intuition: Learning about infinity. Here is the article abstract:

Based on an empirical study, we explore children’s primary and secondary perceptions on infinity. When discussing infinity, children seem to highlight three categories of primary perceptions: processional, topological, and spiritual. Based on their processional perception, children see the set of natural numbers as being infinite and endow Q with a discrete structure by making transfers from N to Q. In a continuous context, children are more likely to mobilize a topological perception. Evidence for a secondary perception of arises from students’ propensities to develop infinite sequences of natural numbers, and from their ability to prove that N is infinite. Children’s perceptions on infinity change along the school years. In general, the perceptual dominance moves from sequential (processional) to topological across development. However, we found that around 11–13 years old, processional and topological perceptions interfere with each other, while before and after this age they seem to coexist and collaborate, one or the other being specifically activated by the nature of different tasks.

Learning about infinity

Florence M. Singer and Cristian Voica wrote an interesting article that was recently published in The Journal of Mathematical Behaviour: Between perception and intuition: Learning about infinity. Here is the article abstract:

Based on an empirical study, we explore children’s primary and secondary perceptions on infinity. When discussing infinity, children seem to highlight three categories of primary perceptions: processional, topological, and spiritual. Based on their processional perception, children see the set of natural numbers as being infinite and endow Q with a discrete structure by making transfers from N to Q. In a continuous context, children are more likely to mobilize a topological perception. Evidence for a secondary perception of arises from students’ propensities to develop infinite sequences of natural numbers, and from their ability to prove that N is infinite. Children’s perceptions on infinity change along the school years. In general, the perceptual dominance moves from sequential (processional) to topological across development. However, we found that around 11–13 years old, processional and topological perceptions interfere with each other, while before and after this age they seem to coexist and collaborate, one or the other being specifically activated by the nature of different tasks.

Multiplication as original sin

Shelly Sheats Harkness and Jonathan Thomas have written an article that is entitled: Reflections on “Multiplication as Original Sin”: The implications of using a case to help preservice teachers understand invented algorithms. This article takes a case report called "Multiplication as original sin" as point of departure. The article was published online yesterday in The Journal of Mathematical Behavior. Here is the abstract of the article:

This article describes the use of a case report, Multiplication as original sin (Corwin, R. B. (1989). Multiplication as original sin. Journal of Mathematical Behavior, 8, 223–225), as an assignment in a mathematics course for preservice elementary teachers. In this case study, Corwin described her experience as a 6th grader when she revealed an invented algorithm. Preservice teachers were asked to write reflections and describe why Corwin’s invented algorithm worked. The research purpose was: to learn about the preservice teachers’ understanding of Corwin’s invented multiplication algorithm (its validity); and, to identify thought-provoking issues raised by the preservice teachers. Rather than using mathematical properties to describe the validity of Corwin’s invented algorithm, a majority of them relied on procedural and memorized explanations. About 31% of the preservice teachers demonstrated some degree of conceptual understanding of mathematical properties. Preservice teachers also made personal connections to the case report, described Corwin using superlative adjectives, and were critical of her teacher.

Multiplication as original sin

Shelly Sheats Harkness and Jonathan Thomas have written an article that is entitled: Reflections on “Multiplication as Original Sin”: The implications of using a case to help preservice teachers understand invented algorithms. This article takes a case report called "Multiplication as original sin" as point of departure. The article was published online yesterday in The Journal of Mathematical Behavior. Here is the abstract of the article:

This article describes the use of a case report, Multiplication as original sin (Corwin, R. B. (1989). Multiplication as original sin. Journal of Mathematical Behavior, 8, 223–225), as an assignment in a mathematics course for preservice elementary teachers. In this case study, Corwin described her experience as a 6th grader when she revealed an invented algorithm. Preservice teachers were asked to write reflections and describe why Corwin’s invented algorithm worked. The research purpose was: to learn about the preservice teachers’ understanding of Corwin’s invented multiplication algorithm (its validity); and, to identify thought-provoking issues raised by the preservice teachers. Rather than using mathematical properties to describe the validity of Corwin’s invented algorithm, a majority of them relied on procedural and memorized explanations. About 31% of the preservice teachers demonstrated some degree of conceptual understanding of mathematical properties. Preservice teachers also made personal connections to the case report, described Corwin using superlative adjectives, and were critical of her teacher.

The fragility of group flow

Alayne C. Armstrong has written an article that was published online in The Journal of Mathematical Behavior yesterday. The article is entitled The fragility of group flow: The experiences of two small groups in a middle school mathematics classroom. Here is the abstract of the article:

This article considers two small groups of students in the same Grade 8 mathematics classroom whose approaches to the same mathematical problem result in very different experiences. Using videotapes and written transcripts, an analysis of the groups’ working processes was undertaken using Sawyer's pre-existing structures required for the presence of group flow, and Davis and Simmt's conditions for complex systems. It is suggested that although both groups had the prerequisite structures in place to experience group flow, the second group was not decentralized enough to enable all members to establish a working collaborative proximal zone of development in which they could develop their ideas as a collective, while the first group was sufficiently decentralized and appeared to demonstrate episodes of experiencing group flow. If teachers are aware of conditions that encourage the experience of group flow, this may help them in forming productive small groups within the classroom and developing successful group-oriented learning tasks.

The fragility of group flow

Alayne C. Armstrong has written an article that was published online in The Journal of Mathematical Behavior yesterday. The article is entitled The fragility of group flow: The experiences of two small groups in a middle school mathematics classroom. Here is the abstract of the article:

This article considers two small groups of students in the same Grade 8 mathematics classroom whose approaches to the same mathematical problem result in very different experiences. Using videotapes and written transcripts, an analysis of the groups’ working processes was undertaken using Sawyer's pre-existing structures required for the presence of group flow, and Davis and Simmt's conditions for complex systems. It is suggested that although both groups had the prerequisite structures in place to experience group flow, the second group was not decentralized enough to enable all members to establish a working collaborative proximal zone of development in which they could develop their ideas as a collective, while the first group was sufficiently decentralized and appeared to demonstrate episodes of experiencing group flow. If teachers are aware of conditions that encourage the experience of group flow, this may help them in forming productive small groups within the classroom and developing successful group-oriented learning tasks.

PeaceJam!

Finally getting around to posting about the PeaceJam Global Call to Action Conference that 4 of my students + myself went to on Sept. 11-13 in Los Angeles.

It was AWESOME.

First of all, if you are not familiar with PeaceJam, check out their website -- it is a great organization, and an awesome thing for kids to be involved in. Nobel Peace Laureates work with youth on service learning projects, and there is an excellent curriculum for the adult educators to help the kids develop their projects.

In their written reflections after the conference, my students said the most memorable part for them was seeing how other teenagers have developed projects to meet needs in their own communities. There were kids there from all over the world doing awesome things, and getting so much love from peace activist superstars.

Aesthetics as a liberating force

Nathalie Sinclair has written an article with the interesting title: Aesthetics as a liberating force in mathematics education? The article was published in ZDM a couple of days ago. Here is the article abstract:

This article investigates different meanings associated with contemporary scholarship on the aesthetic dimension of inquiry and experience, and uses them to suggest possibilities for challenging widely held beliefs about the elitist and/or frivolous nature of aesthetic concerns in mathematics education. By relating aesthetics to emerging areas of interest in mathematics education such as affect, embodiment and enculturation, as well as to issues of power and discourse, this article argues for aesthetic awareness as a liberating, and also connective force in mathematics education.

Aesthetics as a liberating force

Nathalie Sinclair has written an article with the interesting title: Aesthetics as a liberating force in mathematics education? The article was published in ZDM a couple of days ago. Here is the article abstract:

This article investigates different meanings associated with contemporary scholarship on the aesthetic dimension of inquiry and experience, and uses them to suggest possibilities for challenging widely held beliefs about the elitist and/or frivolous nature of aesthetic concerns in mathematics education. By relating aesthetics to emerging areas of interest in mathematics education such as affect, embodiment and enculturation, as well as to issues of power and discourse, this article argues for aesthetic awareness as a liberating, and also connective force in mathematics education.

Read It Here First

Please don't confuse this blog with a breaking news operation. It's hard to be on top of everything amidst being parents, holding full-time jobs, and trying to follow the pennant races (Go Sox!). But sometimes, despite doing most of our blogging after the sun's gone down, we're way ahead of the curve.

Such was the case with the TEACH Grants. Sara was all over this issue back in April, prior to the U.S. Department of Education's release of regulations. I notice that Education Week picked up the story in the September 15, 2008 issue, six months later.

Now, Stephen Sawchuk is an excellent reporter (formerly with EdDaily), but my wife scooped you on this one, dude!!! Check out some of Stephen's blogging at Teacher Beat.

Mathematical imagination and embodied cognition

Ricardo Nemirovsky and Francesca Ferrara have written an article called "Mathematical imagination and embodied cognition" that was published online in Educational Studies in Mathematics on Friday. Here is the abstract of their article:

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing displacements, and (2) articulating necessary cases. The discussion elaborates on the significance of these phenomena and draws relationships with the perspectives of embodied cognition and intersubjectivity.

Mathematical imagination and embodied cognition

Ricardo Nemirovsky and Francesca Ferrara have written an article called "Mathematical imagination and embodied cognition" that was published online in Educational Studies in Mathematics on Friday. Here is the abstract of their article:

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing displacements, and (2) articulating necessary cases. The discussion elaborates on the significance of these phenomena and draws relationships with the perspectives of embodied cognition and intersubjectivity.

Musical Elective Of The Week

After a month-long hiatus following the relocation of the Optimists, Optimist Junior, and Optimist Dog from Madison to Stoughton, Wisconsin, this feature is finally back on track....

The Musical Elective Of The Week Month is The Decemberists.

The city of Portland, Oregon is good for so many reasons. It's one of our favorite places. It has great food, great wine, great coffee, great bread, and great bookstores. Well, maybe not good weather (perhaps that explains the umbrellas?). But it also provides The Decemberists. So that makes up for the occasional rainy day.

The Decemberists are songwriter and frontman Colin Meloy, multi-instrumentalist Chris Funk, keyboardist Jenny Conlee, bassist Nate Query and drummer John Moen. They burst onto the indie music scene with 2003's Her Majesty, The Decemberists and followed that up with 2005's Picaresque which includes the track "We Both Go Down Together". But it probably was The Crane Wife that earned them the immense attention they now receive.

The Crane Wife, released in 2006, is a masterpiece of an album. It's not a collection of songs. It's an album. Inspired by a Japanese folk tale of the same name, the album features "The Crane Wife 3" and the singles "O Valencia!" and "The Perfect Crime #2". It was voted the number one album of 2006 by National Public Radio listeners.

The Decemberists are anchored in Meloy's brilliant songwriting and are fueled by his unique voice and the band's lush instrumentation. As a band, they are hard to categorize musically. They are certainly cerebral, but also can deliver some compelling pop hooks. Without hearing them, perhaps a combination of folk, art rock, and rock is the most apt description.

Expect a new album from the Decemberists sometime in 2009.

The Decemberists will play select dates on the East and West Coasts during the month of November 2008. So, if you're lucky enough to live in those cities, go check them out.

To learn more, check out their web site.

My girl, linen and curls
Lips parting like a flag all unfurled
She's grand, the bend of her hand
Digging deep into the sweep of the sand
--"Summersong," The Crane Wife (2006)

------------------------------------------

Extra Credit--Past Musical Electives of the Week:

Ron Sexsmith
Kasey Chambers
Lucinda Williams
Great Big Sea
Griffin House
Dave Carter & Tracy Grammer
Neil Finn
Ray LaMontagne
Stuart Stotts
Dan Wilson
Kathleen Edwards

SPM 2008 Revision Questions

Times Guides, the publishers of Times Higher Education magazines have published Times SPM 2008 Revision Questions. 15,000 copies of the book were distributed to schools in the Klang Valley and other city centers. In view of making this book available to all SPM students, Times Guides have produced an e-book version of the book for students to download for FREE. The e-book version has questions, answers and past year exam question analysis. This book is produced by a group of experienced teachers who are specialist in their subjects.

The e-book can be downloaded for free here.

Performance and language proficiency

Máire Ní Ríordáin and John O'Donoghue have written an article about The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish. The article was published in Educational Studies in Mathematics two days ago. Here is the abstract of their article:

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

Performance and language proficiency

Máire Ní Ríordáin and John O'Donoghue have written an article about The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish. The article was published in Educational Studies in Mathematics two days ago. Here is the abstract of their article:

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

Gendering of mathematics among Israel Jewish and Arab students

Helen J. Forgasz and David Mittelberg have written an article called Israeli Jewish and Arab students’ gendering of mathematics. The article was recently published online in ZDM. Here is a copy of their article abstract:

In English-speaking, Western countries, mathematics has traditionally been viewed as a “male domain”, a discipline more suited to males than to females. Recent data from Australian and American students who had been administered two instruments [Leder & Forgasz, in Two new instruments to probe attitudes about gender and mathematics. ERIC, Resources in Education (RIE), ERIC document number: ED463312, 2002] tapping their beliefs about the gendering of mathematics appeared to challenge this traditional, gender-stereotyped view of the discipline. The two instruments were translated into Hebrew and Arabic and administered to large samples of grade 9 students attending Jewish and Arab schools in northern Israel. The aims of this study were to determine if the views of these two culturally different groups of students differed and whether within group gender differences were apparent. The quantitative data alone could not provide explanations for any differences found. However, in conjunction with other sociological data on the differences between the two groups in Israeli society more generally, possible explanations for any differences found were explored. The findings for the Jewish Israeli students were generally consistent with prevailing Western gendered views on mathematics; the Arab Israeli students held different views that appeared to parallel cultural beliefs and the realities of life for this cultural group.

Gendering of mathematics among Israel Jewish and Arab students

Helen J. Forgasz and David Mittelberg have written an article called Israeli Jewish and Arab students’ gendering of mathematics. The article was recently published online in ZDM. Here is a copy of their article abstract:

In English-speaking, Western countries, mathematics has traditionally been viewed as a “male domain”, a discipline more suited to males than to females. Recent data from Australian and American students who had been administered two instruments [Leder & Forgasz, in Two new instruments to probe attitudes about gender and mathematics. ERIC, Resources in Education (RIE), ERIC document number: ED463312, 2002] tapping their beliefs about the gendering of mathematics appeared to challenge this traditional, gender-stereotyped view of the discipline. The two instruments were translated into Hebrew and Arabic and administered to large samples of grade 9 students attending Jewish and Arab schools in northern Israel. The aims of this study were to determine if the views of these two culturally different groups of students differed and whether within group gender differences were apparent. The quantitative data alone could not provide explanations for any differences found. However, in conjunction with other sociological data on the differences between the two groups in Israeli society more generally, possible explanations for any differences found were explored. The findings for the Jewish Israeli students were generally consistent with prevailing Western gendered views on mathematics; the Arab Israeli students held different views that appeared to parallel cultural beliefs and the realities of life for this cultural group.

Lesson study in Asia Pacific classrooms

Allan Leslie White and Chap Sam Lim have written an article about the use of the Japanese Lesson Study model in Australian and Malaysian classrooms. The article is entitle Lesson study in Asia Pacific classrooms: local responses to a global movement, and it was published online in ZDM on Wednesday.

If you are interested in the topic, this article gives a nice overview of the history and theoretical background of the Japanese Lesson Study approach, and there is also a nice list of references to dig into. In the conclusions of the article, they claim:

However, the significant features of Japanese Lesson Study, such as the use of collaborative work, working on common goals, sharing of ideas, team teaching, lesson observation and cooperation among peers seemed to exert similar impacts on all groups of participants. Participants from all glocal programs reported an improvement in their lesson planning, better pedagogical content knowledge and closer collegial relationship as a result of experiencing the Lesson Study process.

Here is the abstract of the article:

Japanese Lesson Study is a model for teacher professional learning that has recently attracted world attention particularly within the mathematics education community. It is a highly structured process of teacher collaboration, observation, reflection and practice. The world focus has been mainly due to the work of American researchers such as Stigler and Hiebert (Am Educ Winter:1–10, 1998; The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. Free Press, New York 1999), Lewis and Tsuchida (Am Educ Winter:14–17; 50–52, 1998) and Fernandez [J Teach Educ 53(5):395–405, 2002]. These researchers have documented Lesson Study from the perspective of their social, cultural and educational contexts. In order to develop a deeper understanding of Lesson Study in a post-modern global world, there is a need to seek views beyond those presented from an American perspective. This paper will provide further additional perspectives from an Australian state view and a Malaysian state district view and a university view. The aim is to develop an understanding of how the different contexts have influenced the structure and implementation of the Japanese Lesson Study model.

Lesson study in Asia Pacific classrooms

Allan Leslie White and Chap Sam Lim have written an article about the use of the Japanese Lesson Study model in Australian and Malaysian classrooms. The article is entitle Lesson study in Asia Pacific classrooms: local responses to a global movement, and it was published online in ZDM on Wednesday.

If you are interested in the topic, this article gives a nice overview of the history and theoretical background of the Japanese Lesson Study approach, and there is also a nice list of references to dig into. In the conclusions of the article, they claim:

However, the significant features of Japanese Lesson Study, such as the use of collaborative work, working on common goals, sharing of ideas, team teaching, lesson observation and cooperation among peers seemed to exert similar impacts on all groups of participants. Participants from all glocal programs reported an improvement in their lesson planning, better pedagogical content knowledge and closer collegial relationship as a result of experiencing the Lesson Study process.

Here is the abstract of the article:

Japanese Lesson Study is a model for teacher professional learning that has recently attracted world attention particularly within the mathematics education community. It is a highly structured process of teacher collaboration, observation, reflection and practice. The world focus has been mainly due to the work of American researchers such as Stigler and Hiebert (Am Educ Winter:1–10, 1998; The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. Free Press, New York 1999), Lewis and Tsuchida (Am Educ Winter:14–17; 50–52, 1998) and Fernandez [J Teach Educ 53(5):395–405, 2002]. These researchers have documented Lesson Study from the perspective of their social, cultural and educational contexts. In order to develop a deeper understanding of Lesson Study in a post-modern global world, there is a need to seek views beyond those presented from an American perspective. This paper will provide further additional perspectives from an Australian state view and a Malaysian state district view and a university view. The aim is to develop an understanding of how the different contexts have influenced the structure and implementation of the Japanese Lesson Study model.

Geography: Love and Lies

I've had a love for geography ever since I was toddler. One of my earliest memories is of my paternal grandfather's haggard world map. To help me learn the location of nations and to have some fun, my grandfather wrote onto tiny strips of paper the names of the major countries of the world. Starting around age 3 or 4, I was able accurately to locate nations such as the U.S., U.S.S.R., China, Japan and Australia on this non-political world map, pleasing him to no end.

My grandfather was born on a farm in Ireland -- County Cavan to be specific -- and came "across the pond" as a teenager. Ten years ago, I had the pleasure of tracking down his sole surviving sibling, his youngest sister Teresa (who was a toddler when he left for America, never to return), who still lived in the same village where the family grew up. To date, that was my sole trip to the magical country of Ireland and I will never forget it.

Sarah Palin has been to Ireland, too. Or so she says. Or so her spokesperson says. This "visit" constituted a refueling stop at Shannon Airport in County Claire. This "visit" was offered by the campaign to defend her foreign policy experience. What compelling evidence. Wow.

But wait ... there's more.

Geography whiz and First Lady wannabe Cindy McCain undoubtedly shoots for that blue triangle from the get-go during games of Trivial Pursuit. In an interview with George Stephanopoulos of ABC News, McCain defends Palin's foreign policy experience by noting that "Alaska is the closest part of our continent to Russia." Take that, Joe Biden! (who must undoubtedly be an expert on Bermuda given Delaware's comparative proximity to that island).

Let me stipulate two things:

(1) A visit to an airport DOESN'T constitute a visit to a city or a country. I've been to the Detroit airport countless times (even slept on its floor once), but I've never actually visited the city of Detroit or the surrounding area in Michigan. Even with innocuous time-wasters such as TripAdvisor's Cities I've Visited on Facebook, I don't audaciously claim to have been to Detroit, to Cincinnati or Memphis--or other cities I've connected through. To base your qualifications to be vice-president on such a claim is downright pathetic. Frankly, it calls into question the judgment of the individual who invited you onto the Republican ticket and who wishes to be commander-in-chief.

(2) Proximity DOESN'T equal expertise. A math teacher who teaches in a classroom next to an English teacher isn't better equipped to teach English. A stock broker who lives next door to a mechanic doesn't necessarily know how to fix your carburetor. Living in the Madison, Wisconsin area doesn't make me qualified to lead walking tours of Rockford, Illinois.

What does this all have to do with education? Well, it seems to me that the McCain-Palin campaign doesn't think much of the intelligence of the American electorate by peddling this paltry defense of Palin's lack of foreign policy experience and nonexistent world view. On an intellectual level, I've got to believe that even Republican partisans can see through this flighty logic. If I'm wrong, then we're in some real trouble -- and not just from the potential results of this election.

I guess the moral of this blog post is that geographic literacy by itself isn't sufficient. Truth matters, too. Right, Cindy?

-----------------------------

BONUS: For those of you who haven't discovered PalinDrome yet, just like those MasterCard ads, it's priceless.

Who Says This Election Shouldn't Be About Education?

The staggering economy is clearly hitting working families, investors ... and college students with financial need. The New York Times reports that the Federal Pell Grant Program faces a $6 billion shortfall.

Battered by a worsening economy, college students are seeking federal financial aid in record numbers this year, leading Bush administration officials to warn Congress that the most important federal aid program, Pell Grants, may need up to $6 billion in additional taxpayer funds next year.

Driving the increased applications for federal aid, in part, have been nontraditional students returning to school to improve their job skills during the economic downturn, said Terry W. Hartle, senior vice president for public affairs at the American Council on Education, which represents colleges and universities.

Estimates by the Department of Education suggest that the new president will face an unusually burdensome financing shortfall or the fallout that would accompany trimming the nation’s leading college aid program.

“There are a lot of things going on — more people are applying for student aid, more people are going to college, more people who qualify for the aid are showing up at school,” said Thomas P. Skelly, the Department of Education’s director of budget service, who wrote a memorandum detailing the problem to Congress.

As of July 31, 800,000 more students had applied for grants than on that date last year, according to the memorandum, which called the increase one of the largest ever year to year.

This year, more than six million low-income college students will receive Pell Grants ranging from $431 to $4,731, federal officials said.

Congress appropriated $14 billion for the grants for the current fiscal year, but because of the increase and because of accumulated shortfalls from previous years, lawmakers will need to add $6 billion in new funds next year or cut the size of the grants, Department of Education officials said.

Perhaps the Iraqi government with its oil-driven $79 billion surplus can bail the Bush Administration out of this mess it has created.

Relation between students' behaviors and their mathematical ideas

Lisa B. Warner has written an article that was published online in The Journal of Mathematical Behavior yesterday. The article is entitled How do students’ behaviors relate to the growth of their mathematical ideas? Here is the article abstract:

The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie–Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school problem-solving sessions. The results suggest that certain types of student behaviors appear to be associated with the growth of ideas and emerge in specific patterns. More specifically, as understanding grows, there is a general shift from behaviors such as students questioning each other, explaining and using their own and others’ ideas toward behaviors involving the setting up of hypothetical situations, linking of representations and connecting of contexts. Recognizing that certain types of student behaviors tend to emerge in specific layers of the Pirie–Kieren model can be important in helping us to understand the development of mathematical ideas in children.

Warner focus a lot on the Pirie-Kieren model in her theoretical framework (see the article of Susan Pirie and Thomas Kieren from 1994). The main focus of Warner's article is to address the following questions:

Are different types of student behaviors associated with the growth of mathematical ideas in specific ways? If so, how?

In her conclusions, Lisa Warner suggests that for the students in her study, "certain types of behaviors appeared to be associated with the growth of mathematical ideas in certain ways". She also suggests that further research is needed in order to investigate whether these findings correspond with findings in similar studies of other students, different types of tasks, etc.

Relation between students' behaviors and their mathematical ideas

Lisa B. Warner has written an article that was published online in The Journal of Mathematical Behavior yesterday. The article is entitled How do students’ behaviors relate to the growth of their mathematical ideas? Here is the article abstract:

The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie–Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school problem-solving sessions. The results suggest that certain types of student behaviors appear to be associated with the growth of ideas and emerge in specific patterns. More specifically, as understanding grows, there is a general shift from behaviors such as students questioning each other, explaining and using their own and others’ ideas toward behaviors involving the setting up of hypothetical situations, linking of representations and connecting of contexts. Recognizing that certain types of student behaviors tend to emerge in specific layers of the Pirie–Kieren model can be important in helping us to understand the development of mathematical ideas in children.

Warner focus a lot on the Pirie-Kieren model in her theoretical framework (see the article of Susan Pirie and Thomas Kieren from 1994). The main focus of Warner's article is to address the following questions:

Are different types of student behaviors associated with the growth of mathematical ideas in specific ways? If so, how?

In her conclusions, Lisa Warner suggests that for the students in her study, "certain types of behaviors appeared to be associated with the growth of mathematical ideas in certain ways". She also suggests that further research is needed in order to investigate whether these findings correspond with findings in similar studies of other students, different types of tasks, etc.