This post about inquiry learning reminds me of how much we tend to dichotomize issues, pick teams, and then make a caricature out of the other side. Sometimes we forget our manners when we do this, which, thankfully, Webb does not really do here. Still, I get puzzled by what some people think of as "inquiry" or "discovery learning." My critique (which seems to be shared by many, including Hmelo-Silver, Duncan, & Chinn, 2007) of the Kirschner, Sweller, and Clark (2006) paper is that to them "minimal guidance" really is minimal, assuming that teachers play a passive role in instruction if they're not doing direct instruction. I certainly wouldn't advocate for minimal guidance, nor would I advocate for direct instruction like Kirschner et al. do. There's a middle ground that gets lost too often in our arguments, one that is supported by research. Webb does admit that he is only aware of one major study in favor of inquiry, a 2011 Educational Psychologist paper by Alfieri, Brooks, Aldrich, and Tenenbaum. I wasn't aware of that one, but in these cases I immediately think of the meta-analysis of experimental and quasi-experimental studies by Furtak, Seidel, Iverson, and Briggs (2012). That study found greater learning gains for students in guided or structured inquiry approaches than for students in *either* traditional lessons or minimally guided learning. Furtak's findings support a previous meta-analysis by Schroeder, Scott, Tolson, Huang, and Lee (2007), which also found positives in inquiry-based approaches. Interestingly, the two meta-analyses do not rely on any of the same underlying studies, so when considering how much evidence this represents, it's important to not think of the Furtak et al. and Schroeder et al. work as just two studies, as together they summarize the findings of 98 smaller studies.

Trending Topic Research File: Common Core State Standards

The American Educational Research Association (AERA) has provided a one-page list of the articles published in its journals related to the Common Core State Standards (CCSS). These typically look at differences between the CCSS and prior standards, assumptions of the CCSS, and adoption processes.

First Two Days of School

I have a love-hate relationship with first days of school. On the one hand, I love school. On the other, the first day can be filled with the drudgery of introductions and reviews of syllabi. I cringe to remember one year when I was teaching that I required a significant chunk of the *first 3 days* of class to review my entire syllabus. I somehow convinced myself that if I just explained things clearly enough from the beginning, the rest of the year would go well. I can't say my year went poorly, but I eventually learned that if I wanted a certain kind of mathematical activity and student engagement in my class, my best strategy was to get students involved in those activities right from the start. Fawn Nguyen obviously knows this and I'm happy that she wrote about her approach to the first two days of school.

academic blogs: a labor of love | Punk Rock Operations Research

The vast majority of academics I know do not blog, but I wouldn't use this article to imply they aren't passionate about their work. Mostly, I think they don't blog or use social media in a professional fashion because there aren't norms and incentives for them to do so. That is gradually changing, and as more people find that blogging and social media use benefits their own work, more will engage and become examples for others to follow.

Bill Gates' tech worker fantasy: Column

When we talk about the demand for STEM workers, we should really be talking about the demand for *cheap* STEM workers. There are plenty of reasons to think that we have an adequate supply of people with STEM training and education, but the right people are not always in the right place and willing to work for lower wages. Some of this demand is met instead with foreign workers using H-1B visas.

» Switching to Markdown for scholarly article production The Occasional Pamphlet

I really, really like the idea of writing in Markdown and then using tools like Pandoc to convert to other formats. I tried it and ran into a couple difficulties. First, it's still clunky for me to get citations and references to work anywhere near as smoothly as they do when I use Mendeley's plugin for Word, which puts me just a few keystrokes away from my personal database of 1000+ references. Second, I still need tools for peer editing and I'm not crazy about making them use unfamiliar tools. I love that Draft is built to do peer review, but it's really not built for 50+ page academic documents. My peers use Word and Google Docs and I've found that if I'm required to output Word anyway, putting up with Word during the writing process has been slightly less annoying than worrying about my Markdown conversions and choice of reviewing tools. That said, I'm hopeful that Markdown catches on, as I much prefer writing for the web and screen than thinking I'm still writing for 8.5"x11" sheets of paper.

Imagining Successful Schools -

<blockquote>One of the grand old men of education policy says test-based accountability has got to go.</blockquote> We've put so much emphasis into educational standards and accountability over the past 30 years we seem to have deluded ourselves into thinking that standards and accountability are the essential ingredients in educational improvement, and if we lack improvement, then it must be because we need better standards and more accountability. I tend to agree with Marc Tucker here in this NY Times opinion piece, in what essentially comes down to the adage, "If you find yourself in a hole, stop digging." I think standards are useful, and I can't imagine an accountability-free education system, but it's time for a strategy shift that places more emphasis on teacher professionalism and support.

RRPS picks math instructional material for continuity, rigor | Albuquerque Journal News

The Rio Rancho schools in New Mexico recently did a curriculum adoption for math and chose Eureka Math across the board - from Pre-K through 12th grade. I'm not sure I buy claims of "seamless implementation," and I doubt the curriculum will be in use long enough for any one student to get 13 or more years of it, but I can imagine some benefits from a single K-12 set of curriculum materials. To clarify, that's *in my imagination* and I have no idea if that's the case for Eureka Math.

Mathematics Classroom Observation Protocol for Practices

This classroom observation protocol from the University of Alabama looks at a combination of factors related to student engagement, lesson design and implementation, and class culture based in discourse.

Are math textbooks ready for Common Core? - The Washington Post

One of the reasons it's important for teachers and districts to have some skill evaluating curriculum and its alignment to standards is that you can't always trust the publisher to do their own alignments correctly. Yes, in some cases publisher alignment comes down to slapping a "CCSS-Aligned!" sticker on the cover, but in other cases it can appear to be quite meticulous, with lesson-by-lesson alignments shown in margins of teachers guides or in vast tables with marks where lessons and standards...

What WAS that? or, What was THAT? [#NCTMDenver] | Overthinking my teaching

Christopher Danielson reflects on the final session of #NCTMDenver, a math-love-fest with George and Vi Hart. The talk involved math, it showed off math, it showed a deep appreciation for math, but yet it was difficult to exactly summarize what the talk was about.

Classes should do hands-on exercises before reading and video, Stanford researchers say

I feel like video tutorials have exploded on the web and I remain quite skeptical that a video explaining how to do something is an effective means by which someone should learn. If an animation or other visuals help, then maybe the video works well. But for information that can just as easily be shown statically, then I think video fails to have an advantage. It can even be a disadvantage - case in point, an email I received recently from the university about account security was about 90 second...

Educators Evaluating Quality Instructional Products | Achieve

EQuIP (Educators Evaluating the Quality of Instructional Products) is an effort to build in some quality control when choosing curriculum to meet the Common Core standards. The rubrics are designed to be used at the unit or lesson level; task-level quality judgments are probably best left to domain-specific rubrics like those of cognitive demand in math.

A wakeup call on teacher training - The Denver Post

The National Center on Teacher Quality sometimes gets accused of being an agenda-driven organization, and perhaps that by itself is not a bad thing. NCTQ's vision of quality teacher education - and the means they use to measure it - do not exactly align with those in many schools of education. In Colorado, some programs were made to look worse than they likely are because NCTQ either collected incomplete data or misreported the data they had. Another reason that NCTQ rubs academics the wrong was is tactical - instead of peer-reviewed journals, NCTQ relies on self-published reports accompanies by a massive PR campaign to get their rankings in the hands of journalists who are more than happy to pass it along to the public.

ICME 11 - International Congress on Mathematical Education

At ICME 11 in Mexico in 2008 there was a Topic Study Group for "Research and development in task design and analysis." There are links here to papers that were presented as well as a list of the participants in the TSG.

Assessment Blueprints and Test Specifications

Under most circumstances I'd stick to academic content standards and not use assessment blueprints, but there are exceptions. In the case of PARCC, it's helpful to get some guidance to what high school content might be addressed at Algebra 1 vs Geometry vs Algebra 2, since the Common Core standards themselves don't exactly specify what to expect at each high school grade level.


IMPS is the "Implementing the Mathematical Practice Standards" project from EDC (Education Development Center). Given stories I've heard about the Standards for Mathematical Practice being included in the CCSSM almost as an afterthought, it's interesting to me to see all the attention the SMPs get in comparison to the content standards.

PCMI @ MathForum: Rubric-Implementing Standards for Mathematical Practice

At PCMI, the Park City Mathematics Institute, they have a rubric for the Standards for Mathematical Practice. I like that the rubric separates "task" from "teacher." As *practices*, the SMPs can't be embodied by a task alone but the choice of tasks can predict the likelihood that students will engage in the practices.

SMSG (New Math) Textbooks

If you've heard of the "new math" of the 1960s but don't know exactly what that was, ERIC has a great collection of the "School Mathematics Study Group" (SMSG) textbooks that were at the foundation of new math.

Math = Love: Common Core - Come and Gone: My Experiences as a Classroom Teacher

With new educational standards comes new opportunities for teachers and districts to rethink their curriculum and instruction. Standards can drive change, and often that change isn't exactly specified by the standards themselves. In Oklahoma, the Common Core State Standards had incited change until they didn't, having been repealed by the state legislature. In this post, Sarah Hagan writes about this state of limbo, and her desire to improve with or without the CCSS, while observing the attitudes of some other teachers who never thought the CCSS were anything worth changing for to begin with.

Twitter Math Camp

John Golden shares his Twitter Math Camp experience on one of the NCTM blogs. Part of me regrets not attending since it was within a day's drive, but it felt like too much after other conferences and travel during the summer.

Freudenthal’s “realistic mathematics education” appears to be a fraud | Boycott Holland

The math wars are not unique to the United States. In the Netherlands, routinely one of the highest-performing countries in international mathematics assessments, there is a small yet vocal group who insist that the path established by Hans Freudenthal has been one big mistake. Because I study at the Freudenthal Institute US, occasionally I get anti-Freudenthal writings sent to me. Like the US version of the math wars, the rhetoric can really be over-the-top, with false dichotomies and ad hominem attacks on individuals. In this post, the author makes a claim about something David Tall meant from one of his writings. Tall personally responded to correct the author's interpretation, and the author audaciously replied, "Tall also states that I misrepresent his position. I do not." I honestly laughed out loud at that one, and reminded myself that there's little reason to debate someone who has already decided what you mean regardless of what you say.

‘If only American teachers were smarter…’ - The Washington Post

I fear that some people dismiss Jack Schneider as naive when he suggests that teachers can and should engage more with educational research. Commonly the thought is that the research has to be drastically simplified, watered down, or otherwise repackaged for teachers to accept it, like hiding a child's medicine in his ice cream. I prefer Schneider's optimism and willingness to think creatively about what changes in teachers' routines and resources and the support needed for teachers to get more out of research.

Group to Launch Free Online Reviews of Common-Core Materials - Curriculum Matters - Education Week

As a teacher, I lost count of how many times the question, "Did the neighboring school district like it?" represented the primary quality criteria for education programs and resources. Perhaps it's our decentralized way of structuring our education system, but often we find ourselves lacking in the quality control department. I'm happy to see that some third-party groups are organizing to provide reviews of Common Core-based materials. While the reviews themselves will vary in quality, I think this is an area where we can improve quickly and have some influence over what schools invest in.

How to Teach Kids About Factoring a Polynomial | Edutopia

José Vilson writes in Edutopia about how to teach kids to factor polynomials. The article is a little short for deeply understanding the strategies, but it's still an approach that I really grew to appreciate as a teacher.

A New Ratio for the Japanese Cram School -

International education comparisons are often interesting. In Japan and other Asian countries, it's quite common for students to receive intensive tutoring in the evenings. In math, Japanese students are known for their ability to persist on long problems, seen in this quote: "Yuuki said that after two months, he was now able to solve math problems in 15 minutes, which was something that took him twice or three times as long before receiving private tutoring."

Why Hoboken is Throwing Away All of its Student Laptops - WNYC

1:1 technology programs can be great, but technology has a way of being a solution in search of a problem. The "we bought computers/tablets, now what?" question in this article happens too often, and when there aren't answers (and resources to support ongoing tech use), the 1:1 program can fall apart.

Why Tech Still Hasn't Solved Education's Problems - The Atlantic

This Atlantic article is good for thinking about how learning is mediated by tools and artifacts. In edu-jargon, we talk of tools having "affordances" and "constraints," and technology has plenty of both. We seem to let the technology do what technology is good at, but CPU cycles and algorithms coded in software often underperform in what remains a very personal, social, and human-focused field.

With Fractions, Common-Core Training Goes Beyond 'Invert and Multiply' - Curriculum Matters - Education Week

When I think about blog posts I regret, maybe only one comes to mind: a post I wrote about explaining the "invert and multiply" of fraction division. I showed some kind of proof that really doesn't do much explaining. This post at Education Week does a better job, but I still have some diagrams and explanations in mind that go beyond what's shown here. I don't know how helpful they'd be to others, but maybe I'll finally make that post someday to relieve myself of a guilty conscience.

St. Paul school district weighs later start for high-schoolers -

I consider myself fortunate to have attended a high school that started classes at 8:30, which is considered quite late. In St. Paul, Minnesota, the school district is trying to figure out how to rearrange their buses to allow high school students to start later than their current 7:30 start time. A University of Minnesota study on later start times showed positive effects in attendance, grades, test scores, and mood.