Ah it’s the time of year again. The time of year when we all start looking forward to fireplaces, family, and chewing up reams of your school’s printer-paper by printing out the **Math Blogging Retrospectus**.

The impetus of creating the Retrospectus was that it’s so damn hard to keep up with all the great math teaching content being produced. It’s really difficult to make sure you got all the value out of the math blogosphere when new posts and bloggers pop up every day. Thus, the Retrospectus.

All I’m asking you to do, dear reader, is to **paste a link to one (or two or three or ten) of your favorite math blog posts from 2014 in the comments**. It’s up to you to determine what “favorite” means. Perhaps it was something that you used in your class or want to use in your class. It’s possibly a moving story from a thoughtful facilitator. It could be a post that made you think differently about something, or in a new light.

From last year’s description:

It’s incredibly difficult to keep track of the ever-growing Math Blogosphere. Keeping up with posts is like trying to hold water in your hands. I’m looking for timeless or timely math blog posts that inspired, touched, and/or entertained you. This decidedly NOT a voting thing. It’s NOT a ranking. And for the love of all things holy, it’s not an EDUBLOG award thing. If a blog post touched a single person, I’d like to capture it: chances are it’ll touch another. There are math blogs that I and you do not even know about, but

someone reading this does. Let’s all partake in some shared sharing. Share a link to a few (or several!) blog post that you truly enjoyed, I’ll do some of my patented copying and pasting and attempt to assemble it into a tome that can be downloaded or printed out. They could be short posts on instructional practices or problem ideas. They could be longreads of reflections on teaching and systemic issues. Any and all types are welcome.

I’ll start. Throughout the year, I’ve been bookmarking interesting posts. Here are 10 (and only 10) of them.

- Kate examines the purpose of exams.
- Jonathan gets students to argue mathematically in Pre-Cal. PRE-CAL.
- Chris weighs in on the seemingly-seasonal real-world conversation.
- Ilana recognizes smartness and addresses status issues in math.
- Nora does typical, awesome Nora things. This time with gamifying systems of linear equations.
- Andrew tortures students with a spelling bee in math.
- Nat drills conceptually.
- Michael explores feedback and when it’s best to give (and not give) it.
- Julie gets students to understand the volume of a cone conceptually.
- Sam goes all-in with u-substitution.

Now it’s your turn: post a link in the comments below. If you’ve been derelict in your duties of bookmarking your favorite posts, the @GlobalMathDept newsletter archives might be a goof place to get your footing.

Once you’ve done that, feel free to go back and check out **previous years’ Retrospecti**:

## Critiquing the Common Core on its Merits and Demerits

Criticism of the Common Core State Standards (CCSS) has sadly devolved into theater, when it and schools would benefit from critical analysis. CCSS criticism is all-too-often hyperbolic while CCSS defense delves in dismissal of concerns or even ridicule. That’s a shame because CCSS could use a critical eye: one that understands the standards as an educator and is able to negotiate the good and the bad. A good-faith critique as it were. That’s what I aim to do here as an educator, a parent, and an instructional coach.

Before we get into it, I suppose I should give a full disclosure of all my work-related comings and goings, because that’s apparently a thing that gets called into question these days: I generally support Common Core. I’m a former math teacher (so I naturally gravitate toward critiquing CCSS-Math) who became employed in my current position starting with a grant awarded by the Bill & Melinda Gates Foundation to professionally develop teachers toward CCSS implementation. I’m still employed at the same non-profit, but no longer under that or any grant.

Here are four things I think about CCSS.

1) National standards are basically a good thing, but they do pave the way for mass-assessment.The concern about horizontal and vertical alignment is real. Pro-CCSS folks often point to student mobility from state-to-state as a reason to have nationalized standards, but I’m not even sure you need to go that far. I taught in a district that wasn’t aligned from school-to-school. It would have been nice to have a clear playbook of standards that we were all working from so I knew roughly where kids were (or should be) from day 1.

However, a nationalized set of standards makes it really easy to test and develop tests. While No Child Left Behind (NCLB) was the genesis of national high-stakes testing, a common set of standards may well accelerate it. A nationalized set of standards will make it such that an environment where School X is compared with School Z is inevitable. While I’m a big fan of data generally, that kind of cookie-cutter analysis is troublesome. Even if next generation assessments are “better” (as is alleged, whatever it means), the impetus to benchmark students like crazy will be there.

It’s also true that killing the CCSS won’t end the over-benchmarking of students via standardized test. Neither will scrapping NCLB.2) The standards are generally better than current state standards.I had a conversation this weekend with a Scientist and kindergarten Teacher. We wound up talking a bit about Common Core. The Scientist was mentioning that he saw one of those Facebook posts where the parent shares a confusing worksheet and then it goes viral and then that’s supposed to be evidence that Common Core is dumb. The Scientist, however, said “I saw the worksheet and was like ‘that’s how I do arithmetic in my head.’ The Teacher was a fan of conceptual understanding, promoted in CCSS in a way that until recently was oft absent in state standards.

Conceptual understanding of numbers and number-sense is crucial for (among other reasons) future Algebraic understanding. CCSS attempt to get at that. However, it leaves many parents – even educated parents – frustrated. Within the past few weeks I’ve had to google “Story Mat”, “Base 10 Drawings”, and “bar model” – which aren’t even in the Common Core Math standards, but rather, idiosyncratic terms developed by curriculum publishers – to help my daughter with her math homework, and I’m allegedly some sort of math expert. I’ll admit it’s frustrating, and there will be a gap between those of use that learned procedurally and those that are learning conceptually. Still, the ability to break apart numbers and recombine them is an essential mathematical skill.

Moreover, state standards are often kind of a mess. They can be a mish-mash of best-intentions, over-prescriptive, lengthy, poorly-aligned, and not terribly well thought-out or research-based standards. Sometimes they look like the worst of things that were invented by committees. I can primarily speak to the context I taught in (Texas), but I’ll say that CCSS-M are fewer, cleaner and simply better standards than the ones I had to wrestle with. There’s an emphasis on reasoning and conceptual understanding that wasn’t there in the previous generations’ standards.

It’s interesting that Indiana, which opted out of CCSS, has adopted standards that look conspicuously like CCSS. It’s one reason that I’m optimistic that even if CCSS becomes so politically toxic that all states abandon it, it will still have been for the greater good. The folks actually in charge of standards and standards-writing generally see the good that CCSS has to offer.

3) Common Core has had an awful rollout strategy and has been accompanied by virtually non-existent training.The Teacher in the aforementioned conversation was a fan of Common Core, but did describe that many of her colleagues were struggling to teach math conceptually rather than procedurally. That’s 100% understandable given the means of CCSS rollout, which wasn’t much of a rollout at all.

I can’t say exactly what the “correct” rollout would have looked like, but it wouldn’t have been this. Teachers are often left to interpret and teach the new standards on their own. There’s a gap between how teachers (and you and I) learned (or didn’t learn) math and how teachers are expected to teach. Almost every teacher working today was trained in a decidedly non-CCSS pedagogical environment.

While that’s understandable in any seismic shift in education standards, what’s inexcusable is the lack of time and resources devoted to professionally develop teachers, particularly at the federal level. Race To The Top (RTTT) is kind of ridiculous as an avenue to professionally develop teachers: “show us that you can demonstrate proficiency in Common Core and then we’ll give you money to develop teachers to teach using Common Core State Standards.”

What’s worse is that many states and districts are tying teacher pay and employment to success on standardized assessment. And they’re doing it now, instead of after a few years of trial! I’ll be honest, if I knew my employment was tied to my students being successful on a math assessment, I’d probably “play it safe” and try to push as much algorithmic instruction as possible as a temporary band-aid rather than try a new avenue of fighting for conceptual understanding. So there may even be a misalignment between the current instruction and the current standards.

There have been disparate tools here and there to help teachers out, but no nationalized training or systemic interpretation. It’s been largely grant-based which is, by nature, sporadic and not systemic. Pro-CCSS folks like to chortle at the vitriol directed toward Bill Gates for awarding CCSS-related grants, but grants as a mechanism to drive systemic and ubiquitous change is a sketchy proposition.

But once again, my optimism shines through: now that math education programs and teacher training programs actually

havestandards (good ones!), they’ll hopefully start being able to prepare teachers properly. There will certainly be a lag time.4) There are legit concerns about the appropriateness of grade-specific domainsI’m uncomfortable suggesting that “Every student should know how to do X by the end of first grade.” Kids do come in at very different levels. What’s confusing about CCSS (Math) is that after Grade 8, they do away with grade-specific standards and give general domains such as “High School: Interpreting Functions” and “High School: Number and Quantity”. It’s as if after 8th grade, suddenly students and schools have the agency to figure it out on their own.

I appreciate having those benchmarks of what students “should” know by the end of each grade. However, the consequences of students not being able to demonstrate proficiency on those standards – particularly in the early grades – can be disruptive. And while Pro-CCSS folks would argue that we need to separate the standards from the assessments of those standards, the assessments and consequences are a natural outcrop of nationalized standards. One naturally follows the other. And I’ve no idea how to alleviate those consequences. Districts, States, and the DOE will not simply afford more resources to schools with students that fail to meet those standards. They’ll shut them down. Common Core State Standards is part of a system that potentially greases the skids for school closures and community disruption. These disruptions are essentially mandated in NCLB as federal law, before the CCSS existed. My fear is that CCSS will be used as the tool that NCLB uses to disrupt communities.

It’s also not fair to pin blame on the standards themselves. The goal was to develop a set of national, easy-to-follow, research-based, appropriate standards that would ensure students would build toward conceptual understanding of mathematics and problem solving, and I believe they achieved that goal.

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I’m not terribly optimistic about the long-term sustainability of CCSS as a national set of standards. Steve Leinwand once said that if Common Core becomes political, it’s dead in the water. It’s certainly political now (even if it doesn’t really move the needle electorally). I am optimistic that the folks in charge of evaluating and writing standards, such as those in State Departments of Education, have tended to see the importance of conceptual understanding, among other things.

I’m hopeful that 10 years from now either A) my concerns and the concerns of others will have been addressed or B) the residual of the failed-implementation of CCSS remains embedded in state-level standards. Either way, it’s about time we have a conversation about Common Core that is based in actual teacher input and student outcomes.

(I’m happy with comments on this post with the intention of continuing conversation. But c’mon, hysterical comments have no chance of getting published.)===

Thanks to Christopher, Tracy, and Mike for their feedback on this post.