Raymond C. Johnson

Annual Meeting - Saturday, April 20, 9:30 am

Frank K. Lester - Indiana University

Frank Lester was the editor of the 1234-page Second Handbook of Research on Mathematics Teaching and Learning. This was an interesting talk, not so much for any specific content but for how it was put together. Lester began the talk by demoing Algebra Touch, an iOS app that promotes fluency with symbol manipulations in solving equations. He asked, "What will the math classroom of the future be like?"

Lester: "The teacher's job is to make students better at being productive when they don't know what to do." #NCTMDenver
— Raymond Johnson (@MathEdnet) April 20, 2013

A snail is at the bottom of a well that is 10 meters deep and it wants to get out. Every day it climbs up 4 meters. It then slides back 2 meters when it rests at night. If it does this day after day, how many days will it take the snail to reach the top of the well?

Annual Meeting - Saturday, April 20, 8:00 am

Christopher Danielson - Normandale Community College, Bloomington, Minnesota

As Steve Leinwand noted in his Thursday talk, math teachers are a relatively conservative, risk-averse bunch. Perhaps our conservatism comes from the perceived slow but steady progress of math over millennia where it's easy to take comfort in the old because the new can seem so difficult to obtain. Some of this rubs off in the way we teach, the activities we choose for students, and our judgement about what's important for students to know.

Chris Danielson's session kicked off by calling out some mathematics that gets taught in the name of "needing it for calculus," despite no widespread need for it anymore. Simplifying radicals. Rationalizing the denominator. Simplifying rational expressions. Factoring quadratics. Composition of functions. The binomial theorem. It's not that someone, somewhere doesn't have a use for these things, but what is increasingly becoming the exception should not prove the curriculum rule. Mediocre proficiency with these topics is not what leads students to be successful in calculus. What students really need for calculus is a deep understanding of slope as a rate of change and accumulation.

Annual Meeting - Friday, April 19, 3:30 pm

Francis (Skip) Fennell - NCTM Past President; McDaniel College, Westminster, Maryland
Jon Wray - NCTM Board of Directors; Howard County Public Schools, Ellicott City, Maryland

Skip Fennell, Jon Wray, and Beth Kobett (who was absent for this presentation) are the leads on ems&tl, the Elementary Mathematics Specialists & Teacher Leaders Project. As the name implies, the focus here is on supporting math specialists, such as district-level curriculum directors, instructional coaches, and anyone who is in a position to support mathematics teachers.

For this presentation, Fennell and Wray looked at the upcoming Common Core assessments, PARCC and Smarter Balanced (SB), and suggested ways math specialists can help teachers prepare for the tests.

Annual Meeting - Friday, April 19, 2:45 pm

NCTM Professional Development Services Committee
Chonda Long, Director of Professional Development at NCTM

The take-away from this session is pretty simple. To help facilitate professional development, NCTM has produced a series of free, online reflection guides that leverage lessons in NCTM journals.

Annual Meeting - Friday, April 19, 2:00 pm

Christian R. Hirsch - Western Michigan University

Hirsch might claim that modeling is at the core of the Common Core, but at a glance it looks like a standard without standards. Yes, the fourth Standard for Mathematical Practice is "Model with mathematics," but the high school content standards chooses to mark standards in other domains as related to modeling instead of grouping the modeling standards together. This makes it more difficult to see the modeling connections across the high school standards, but that shouldn't reduce their importance.

Christian Hirsch has been at Western Michigan for 40 years and he is probably best recognized as the principal investigator for the Core-Plus Mathematics Project. Along with IMP, Core-Plus is one of the most recognized secondary, integrated, NSF-funded curricula to come out of the post-Standards curriculum development period in the 1990s.

Annual Meeting - Friday, April 19, 11:00 am

Emily Thrasher - North Carolina State University
Ayanna Perry - North Carolina State University

At NC State University there is a program called the Noyce Mathematics Education Teaching Scholars, funded by the National Science Foundation. Along with providing preservice preparation, this program experimented with using online tools to support their graduates (called "Scholars" below) in their first years of teaching.

Annual Meeting - Friday, April 19, 9:30 am

Steve Leinwand - American Institutes for Research, Washington, D.C.

There is perhaps nobody better at shouting math education's rallying cry than Steve Leinwand. Knowing that my notetaking could not keep up, I recorded Steve's talk for later review. Graciously, Steve has granted me permission to post it here. (Which saves me a ton of typing!) You can find slides for Leinwand's "Tilling the Soil" talk on his website.


Check this out on Chirbit

Dan Meyer covered the tweeting duties during the talk:

“Anyone who teaches multiplication by anything but partial products should be drawn and quartered.” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

“Algebra II is an insipid course. It’s connected to nothing in the real wold.” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

“But we love Algebra II. It put hair on our chest twenty years ago.” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

“The most imp. 9 words in the CCSS are ‘Construct viable arguments and critique the reasoning of others.'” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

“Show me a class where SMP3 happens and I’ll show you a class where the other practices are happening.” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

“Standards don’t teach. Teachers teach.” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

Recommending learnzillion.com videos if you want an image of particular standards. /by @steve_leinwand #NCTMDenver /cc @jonathanwray
— Dan Meyer (@ddmeyer) April 19, 2013

“My kids are going to have to demonstrate the standards like THAT?!” Encourages you to head to SBAC and PARCC sites. @steve_leinwand #NCTM13
— Dan Meyer (@ddmeyer) April 19, 2013

“We need PD that supports a culture of collaboration.” Banging a loud drum for coaching and peer observation. @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

“Everyone tapes themselves once a month and one is played/critiqued randomly at staffmeeting.” On practices at good schools. @steve_leinwand
— Dan Meyer (@ddmeyer) April 19, 2013

“We have standards for practices and content. Where are the standards for implementation?” /by @steve_leinwand #NCTMDenver
— Dan Meyer (@ddmeyer) April 19, 2013

Annual Meeting - Thursday, April 18, 2:45 pm

Mieke Abels - Freudenthal Institute for Science and Mathematics Education, University of Utrecht
+Michael Matassa Jr. - Freudenthal Institute US, University of Colorado Boulder
+Raymond Johnson - Freudenthal Institute US, University of Colorado Boulder

When it came time to propose session for the 2013 NCTM Annual Meeting in nearby Denver, we at the Freudenthal Institute US at CU-Boulder knew we should have some kind of "Intro to RME" workshop. Because I was already proposing to be a lead speaker on another session, I needed to find someone else to take the lead. Michael Matassa said he would do it, but then +David Webb had a better idea: Why not ask Mieke Abels from the Freudenthal Institute to do it? Mieke would be a perfect choice - she's been involved in FIUS from the beginning and she continues to be involved in curriculum development for Mathematics in Context and curriculum in the Netherlands. Happily, Mieke agreed and Michael and I were happy to back her up as co-presenters.

• Mathematics in Context (MiC) - units used here were "Comparing Quantities" and "Graphing Equations"
• Mathematics in the City (MiTC) - unit used here was "The California Frog-Jumping Contest"
• Contexts for Learning Mathematics
• Digital Mathematics Environment (DME) - for balance problems, login as guest then Math Secondary Education -> Algebra -> Lesson - System of Equations (Netherlands-based website, more information)
• 4th International RME Conference, September 27-29, 2013, in Boulder, CO - see fius.org
• Utrecht Summer School on Mathematics and Science Education, August 19-30, 2013
• Paper: From Informal to Formal, Progressive Formalization an Example on "Solving Systems of Equations" by Martin van Reeuwijk (citation below)
• Link to slides (pdf, pptx) and handouts

Annual Meeting - Thursday, April 18, 1:00 pm

+Raymond Johnson (Me!) - University of Colorado Boulder and Freudenthal Institute US
+Susan Thomas - University of Colorado Boulder

Grade 6: Variability and Distribution

• Mean, Median, Mode, and Range
• College Athletes
• How Long Are Our Shoes? (ASA link)

Grade 7: Sampling and Inference

Grade 8: Covariation

Research Presession - Wednesday, April 17, 1:00 pm

Janine T. Remillard - University of Pennsylvania
Ok-Kyeong Kim - Western Michigan University
Luke Reinke - University of Pennsylvania
Napthalin A. Atanga - Western Michigan University
Joshua Taton - University of Pennsylvania
Dustin O. Smith - Western Michigan University
Hendrik Van Steenbrugge - Gent University
Shari Lewis - Aquinas College

This group, composed mostly of scholars from the University of Pennsylvania and Western Michigan University, reported on the findings of their ICUBiT project. The project, "Improving Curriculum Use for Better Teaching," has the goal of better understanding how teachers interact with their curriculum materials to design instruction. Using Brown's (2009) concept of pedagogical design capacity, the study looked at teachers using five different elementary curricula and assessed teachers' knowledge of the mathematics embedded in curriculum materials. The five curriculum were Everyday Math, Investigations, Math in Focus, Math Trailblazers, and Scott-Foreman.

Using interview data, curriculum logs, video recordings, field notes, pre-observation check-ins, and two teacher content knowledge assessments, the group looked for teacher actions and understandings related to transitions from the written to intended and intended to enacted curriculum (Stein, Remillard, & Smith, 2007). This was also related to fidelity of curriculum implementation and in-the-moment decision making.

Research Presession - Plenary Session - Wednesday, April 17, 10:30 am

Jo Boaler, Stanford University

"I think math is the subject with the greatest gap between what we know works from research and what happens in classrooms."

Jo Boaler used her plenary session as a plea to the research community to not only do good work with their research, but to find ways to make it more shareable. "New knowledge is not enough," says Boaler. As part of a presentation she made at ICME in 2006, she surveyed teachers from countries around the world, asking, "What research study has made the biggest impact on your practice?" She found that in the Netherlands, the Freudenthal Institute has a huge impact in classrooms, and the Centre for Research in Pedagogy & Practice has a similar impact in Singapore. But often in other countries, including the U.S., teachers often cannot tie any of their practice to an influential body of research.

That doesn't mean that U.S. research hasn't had an impact on practice. When Boaler asked math ed researchers, Jeremy Kilpatrick pointed to Cognitively Guided Instruction (CGI) for having a long history of helping elementary teachers and their students. Boaler found other examples, but they were all from elementary. She suspected that elementary teachers are both eager to learn about students' mathematical learning, and they recognize the enormous capacity for learning they see in elementary students.

Boaler pointed out one of the tensions of sharing research: Just as we know students don't learn simply because we tell them something, teachers don't learn simply because we hand them a journal article. "I am really sure that teacher learning, one thing about it, needs to be generative and we need to be giving teachers things they can take back to their classroom and continue to learn from." Boaler also recognized doing research in partnership with teachers is probably the gold standard, both for identifying questions that are really important for teachers and working along side them.

Boaler stressed the need for "records of practice," including student work, curriculum materials, videos of classroom teaching, teacher notes, and assessments. "The most powerful impact I've had comes from showing these records of practice." As an example, Boaler showed a video of two classrooms in the same high school. The first classroom, as a result of the math wars, was a class that reverted from using IMP to a traditional approach. The teacher in the classroom is talking while they work out an example, and students sit quietly in rows. Engagement is passive -- at best, the students are listening. The second video Boaler showed was from a classroom down the hall. They were working a problem of a skateboarder spinning off a merry-go-round towards a wall, and the engagement in that classroom was much different. Before the students had solved the problem, the teacher stopped students to share their strategies. Students were active at the board and at their desks, questioning each other or reaffirming each others' strategies.

Using Research to Make a Difference

• Work harder and more intentionally to translate and communicate research to teachers and the public
• Engage with different forms of media
• Stand up to unethical behavior and academic bullying
• Work as hedgehogs, foxes, and hedgefoxes to make math classrooms places in which all students thrive

Research Pressession - Wednesday, April 17, 8:30 am

Geoffrey B. Saxe - University of California, Berkeley
Maryl Gearhart - University of California, Berkeley
Ronli Diakow - University of California, Berkeley
Nicole Leveille Buchanan - University of California, Berkeley
Jennifer Collett - University of California, Berkeley
Bona Kang - University of California, Berkeley
Kenton De Kirby - University of California, Berkeley
Marie Le - University of California, Berkeley
Discussant: Deborah Loewenberg Ball - University of Michigan

This group from Berkeley presented their findings from the use of Learning Mathematics through Representations, or LMR. LMR is a research-based curriculum unit for the teaching of integers and fractions in the elementary grades. Despite only being 19 lessons long (at the time of their study), it carefully attended to students' definitions of number, unit intervals, subintervals, and early fraction sense. When compared to similar coverage by Everyday Math, LMR produced significantly higher learning gains at all stages.

1. What are you learning about teaching?
2. What are you learning about the challenge of "drop-in" curriculum?
3. What are you learning about the assessment of student learning?
4. What did you learn about who was talking in class? What were the relationships with social or identity markers? What are you learning about the use of problems that weren't situated in the real-world of the students?
5. How can the rest of us learn how to do this kind of programmatic work?

Research Pressession - Tuesday, April 16, 3:00 pm

Pat Herbst - University of Michigan
Daniel Chazan - University of Maryland
+Karl Kosko - Kent State University
+wendy rose aaron - Oregon State University
Justin Dimmel - University of Michigan
Orly Buchbinder - University of Maryland
Ander W. Erickson - University of Michigan

There are many things about teaching that can be described, but some very important things can be very difficult to measure. This group is working on creating an infrastructure and set of methods to make quantitative claims about phenomena in teaching, such as teacher decisions, recognition of norms and obligations  mathematical knowledge for teaching, and teacher beliefs. Developing these methods should help get the field beyond "what works" to a place of "how things work," ideally resulting in a model where we can better justify certain teaching practices and predict the results of their use. In addition to exploring interventions in classrooms, or working with teachers watching videos of classrooms, the group is using LessonSketch, a cartoon-like technology that allows users to quickly create and/or watch classroom scenarios.

There are several aspects to this research. First is looking at the breaching of norms. Using LessonSketch, teachers watched animations of classroom practice and "pinned" instances of norms being breached. The group found that participants were more likely to pin and remark on actions that breached norms, with more experienced teachers being more adept at identifying the breaches.

Research Presession - Tuesday, April 16, 1:00 pm

Alison Castro Superfine - Learning Sciences Research Institute, University of Illinois at Chicago
James Lynn - Learning Sciences Research Institute, University of Illinois at Chicago
Timothy Stoelinga - Learning Sciences Research Institute, University of Illinois at Chicago
Mara Martinez - Learning Sciences Research Institute, University of Illinois at Chicago
Cynthia Schneider - Charles A. Dana Center, University of Texas at Austin
Diane Briars - Pittsburgh, Pennsylvania
Discussant: Phil Daro, Public Forum on School Accountability, San Francisco

Algebra 1 continues to be a make-or-break-it course for many high school students. Some 75% of students who fail Algebra 1 will also fail on a 2nd attempt, or to get them through they will be placed into a pseudo-algebra course that grants credit without the rigor and support.

This project arose from the need to find a different way to deal with struggling algebra students. With NSF, Chicago Community Trust, and Gates Foundation funding, this group worked as a design team consisting of 25 researchers, curriculum developers, and practitioners to develop and oversee an intensified algebra program where students take algebra two periods each day. The key partner was the Dana Center at Texas at Austin, and you can find the project website at http://www.utdanacenter.org/intensifiedalgebra/index.php. Much of what was described in the presentation can be found in the key design features and course and lesson structure.

Research Presession - Tuesday, April 16, 8:30 am

Anne Foegen - Iowa State University
Barbara Dougherty - University of Missouri, Columbia
Vickie Spain - University of Missouri, Columbia
Jeannette Olson - Iowa State University
Subha Singamaneni - Iowa State University

One of the essential challenges in measurement is to design an instrument that captures the maximum amount of information using a minimum amount of time and resources. (Hint: You can't have both.) While I agree with Lorrie Shepard (2000) that "good assessment tasks are interchangeable with good instructional tasks" (p. 8), there can be room for other kinds of assessments for specific purposes.

This collaboration between researchers at Iowa State University and the University of Missouri, Columbia, is attempting to develop a set of algebra assessments for progress monitoring that students can take in a matter of minutes and can be graded by a teacher equally quickly. Part of the goal is to create the kind of progress monitoring instrument that would be useful for Response to Intervention (RtI). It's definitely something that is needed, as I remember once being told I had to use a simple arithmetic assessment for RtI (for high schoolers!) because an algebra version did not exist for the RtI system the district was using.

We spent time in this discussion session talking about the tasks on both the procedural and conceptual progress-monitoring instruments. While some of the problems were certainly interesting in the way they tried to address student thinking, most of the instruments looked very, very traditional. There is a heavy focus on symbol manipulation and almost nothing comes associated with even a hint of context. Yes, a math student with strong formal skills would do well on these assessments, but I couldn't help but think they're missing something in their approach. That feeling was probably best summarized with the question I asked them: "This assessment looks like something designed for students of Saxon textbooks. How would you feel if that is the case and your instrument is used to promote Saxon texts?"

I left reminding myself two things: (a) projects at the end of the first of a federally funded project are still very much at the learning/big revisions stage and (b) they wanted a test that could be taken in 5-7 minutes, and they got one. If there's something impressive about this effort, it's probably that this team seems to have come to grips with the reality of sacrificing some quality for efficiency. They're pushing themselves to make the best <10 minute algebra tests they can, and I hope their end result is useful, or, failing that, helps us better understand practical limits of assessment.

Braving the snow, Ryan Grover and I slogged our way via RTD from Snowy Boulder to Almost-as-Snowy Denver. We arrived in time for a poster session. If you're unfamiliar with poster sessions, I'd describe them as a sort of academic mingling punctuated by awkward moments of silence as you read people's posters before deciding if the person is worth talking to. Yes, it's as fun as it sounds. I had one extended conversation with Sara Lohrman Hartman from Ohio University. Her recent dissertation work in rural Appalachia studied how a small school utilized a math coach. That's a rare luxury for a small rural school, at least in my limited experience.

As 7:00 neared I made my way to the plenary session and happily found Amanda Jansen standing outside the door. I'd never met Amanda in person, but I've conversed with her regularly on Google+ for more than a year. In that time she's made time for me and put up with my questions and rambling; it may not mean much to her, but as a grad student it means a lot to be welcomed by others in the field. We took some seats midway back in the room and settled in for a talk from Kenneth Zeichner, a well-known expert in the field of teacher education. His talk was not specific to mathematics education, but still of great interest for anyone who cares about how teachers are prepared and the institutions that prepare them.

As a student in Jennie Whitcomb and Dan Liston's Research on Teaching and Teacher Education class this semester, Ken's talk was very familiar. (If you've ever been told of the importance of reflective teaching, Ken and Dan literally wrote the book on the subject.) Ken began by framing three perspectives in the current debate about teacher education. First are the defenders, those who want to preserve the function and status of college and university-based teacher education (UBTE). Next are the reformers, those who seek to deregulate teaching and let the quality of teachers and teacher preparation be dictated by free market principles. Ken frequently cited Rick Hess as a proponent of this perspective, and shared George Will's belief that closing ed schools was the surest path to improving education in the U.S. Last are the transformers. This group, and where Ken places himself, wants reform of teacher education, but in a way that builds upon the capacity and expertise of UBTE and preserves a democratic, public system not driven by market forces.

From here, Ken shared what he sees as the two visions for preparing quality teachers. One is a system that produces professionals for a teaching profession; the other is a system that is technocratic and highly skill-driven, with teachers focused on actions that raise test scores in a narrow curriculum. Teaching skill is important, admits Zeichner, but professionals go beyond the management of a classroom to understand the social and political context of schools and their communities, and have skills that allow them to better reflect in ways that positively impact their teaching.

There are about 3.6 million teachers in the U.S., and alternative pathways for training those teachers (TFA, teacher residency programs, etc.) have grown since the early 1990s. Still, somewhere between 70-80% of the nation's teachers have earned licensure through UBTE at one of the almost 1400 college- and university-based programs around the country. Even if we were to deregulate teacher education, the market does not (and probably would not) have the capacity to prepare teachers without the help of UBTE.

Zeichner admits that UBTE has gotten a lot of non-critical, negative attention from the media. We've come to believe that too many teachers are not getting good results and efforts are now underway to trace poor student results back to the programs that prepared the teacher in those classrooms. When a recent bridge collapsed, said Zeichner, "The engineer who designed the bridge was exposed in the media but I don't remember anyone asking what engineering school he attended." Using another analogy, Zeichner said judging teacher education this way was similar to the idea that we should judge medical schools by patient outcomes. The result, says Zeichner, would be doctors avoiding treating those who need treatment most, just as teachers will avoid teaching in the tough schools with histories of poor test scores. This will lead to further inequality in how quality teachers are distributed, something the U.S. -- which was recently ranked 26th out of 29 nations in a UN report about child well-being -- cannot afford to have happen. The reformers' cries of "No Excuses!" does not rid us of the ails of poverty, no matter how good the teachers might be.

Zeichner addressed some key contradictions in the teacher education argument. For example, the Obama administration has pushed for higher standards for students while simultaneously pushing for alternative pathways to teaching that have lower standards. Also, as Mike Rose has pointed out, the logic of removing teacher education requirements and regulation, or to disregard teaching experience as a measure of quality, makes little to no sense in any other field. (Nobody would trust a neurosurgeon who hadn't been properly trained and lacked experience.) Further, no high-achieving country has deregulated their system of teacher education. Countries like Finland and South Korea have set their standards high, not lowered them.

Zeichner admits that messages like this, and his affiliation with schools of education, have led many to see him as a defender of UBTE. Zeichner insists that he's not a defender, but a transformer. Instead of deregulating UBTE, he sees a great need to change, yet not replace, our current system. This transformation would shift UBTE closer to the world of practice, providing a clinical experience for preservice teachers in a hybrid approach. This move would require the sharing of responsibility and accountability for teacher preparation with schools and their communities, a shared space with values that would prioritize democratized knowledge. Zeichner never advocated for this as a cure-all, but it is the approach most likely to support a system of effective, professionally prepared teachers.

Q&A

(Note: These quotes from Zeichner are rough approximations. Caveat emptor.)

Q: An attendee from Chicago asked about the dismantling of public education in Chicago and the closing of public schools in lieu of charters.

Zeichner: "I'm not against charter schools. I'm against disempowerment of parents and local stakeholders." Zeichner says he was seeing similar school closings in his home of Philladelphia, where public schools are being closed and replaced by charters run by charter management operators. A new study should be out soon that shows the ineffectiveness of these approaches so far. "There's a lack of democratic debate. I'm not for the alternatives to go away, but I'm for an honest debate."

Q: Why do educational entrepreneurs think they're going to make a lot of money?
A: Zeichner: "Some alternative routes use non-profit status for the tax breaks and they outsource their services. From a distance it's hard to see where they're making money, but they are. ... I'm not implying anything about morality. Greedy, self-serving attitudes are everywhere, including universities. But there is a lack of transparency about what's going on. It astounds me how the NewSchools Venture Fund has so much influence while flying under the radar."

Q: I've done UBTE and "quick fix" teacher education programs. Quick fix doesn't work, and online programs are dangerous. Still, too many teachers don't really their profession like a true profession.
A: Zeichner defends online education to a degree, having been involved with some online programs that offered a lot of quality. "I'd be careful in discounting all online programs. Some universities are using them along with more traditional approaches. They can be improved and we still have a lot to learn. We need to be careful about demonizing anything just based on their sponsorships or affiliations."

Q: What are things a new generation of mathematics educators should fight for in public education? How do we take our conversations outside the education community?
Zeichner: "For me, I've decided that ed schools alone will not accomplish much. The ownership of teacher education needs to be broader and shared with communities. I recently met with a lot of stakeholders and listened to their stories. There's a lot of community activism in places like Chicago and Philadelphia, and we can join those efforts already underway instead of coming in from above with solutions to their problems. I wish I'd been more in the public sphere in my career, writing more op-eds and participating in forums, even if many would have disagreed with me. Now, the polarization we're left with is harmful."

Q: How do we measure low-performing teacher education programs?
Zeichner: "I agree with the National Research Council's report on improving teacher education, and that the profession itself needs to take care of its own accreditation and monitoring. I'm afraid that test scores and value-added models will fill this role at great cost and distraction, as simply ranking as a way to improve quality has never really worked. To anoint these people who know little about the field as saviors is idiocy. Twenty-five years from now people will look back and wonder how we could have been so stupid."

(Mic drop. Not really, but I wish.)

My Thoughts

For me, Zeichner's serious (and some might say somewhat depressing) talk was balanced by a sense of validation. Not only did I recently write a paper that expressed many of these same ideas, it gives me hope that the system I'm a part of is recognizing a need and possibility for significant change. For some people, I'm sure a reformed/deregulated system of teacher education seems like a remote possibility, but right now in Colorado we're anticipating the introduction of legislation proposing to do exactly that, removing the requirement for teacher education as we know it. If that bill appears and makes progress, you'll be sure to hear more from me.

It's going to be a busy, busy week. The advantage of having a major conference in your backyard is that you feel like you can go to everything, but the disadvantage is the feeling you should be going to everything despite local distractions and responsibilities that don't go away. I try to get my money's worth at conferences; I think when I went to the Annual Meeting in 2008 in Salt Lake City I attended 17 sessions across the four days. We'll see if I set a new personal record this year. I'll be attending both the Research Presession and the Annual Meeting and have attempted to describe my schedule below.

RME at NCTM

Tuesday

Thursday

Friday

Saturday

My Schedule

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Few things brighten my day more than seeing math teachers on social media seek out research:

@doingmath @natbanting Thanks! I think @nik_d_maths and I should include a classical education piece in our journal each month.
— Chris Robinson (@absvalteaching) March 29, 2013

Getting the Article

I should begin by first disclaiming that while I'm generally pro-standards, I'm also somewhat agnostic about standards. How can that be? Without going into much detail, I believe (a) what we "count" as mathematics is socially determined and standards documents are just part of that determination, (b) I will never perfectly agree with a standards document, but the amount of agreement should not be underestimated, and (c) if there's any power to standards, it's in how they're implemented -- and "good implementation" is very likely to be seen as just "good teaching" under a different set of standards, or no standards at all. It is with this mindset that I watch with some amusement (and sometimes, disappointment) arguments against the Common Core State Standards because of some poorly designed accountability measure. I'm pretty sure poorly designed accountability measures would be a concern right now regardless of the standards in place.

Still, I occasionally see things in the Common Core math standards (CCSSM) that make me stop and wonder, "How are teachers going to deal with this?" One recent instance of that was with how the CCSSM addresses the topic of absolute value. As I looked through Discovering Algebra: An Investigative Approach, I saw the typical "distance from zero" definition followed by an investigation that included this rather unhelpful picture and caption:

Grade 6

CCSS.Math.Content.6.NS.C.7 Understand ordering and absolute value of rational numbers.
CCSS.Math.Content.6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
CCSS.Math.Content.6.NS.C.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3oC is warmer than –7 oC.
CCSS.Math.Content.6.NS.C.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
CCSS.Math.Content.6.NS.C.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
CCSS.Math.Content.6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

and

CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Grade 7

CCSS.Math.Content.7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

and

CCSS.Math.Content.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Grade 8

High School

CCSS.Math.Content.HSN-VM.C.12 (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

CCSS.Math.Content.HSA-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

CCSS.Math.Content.HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Conundrum

"Regardless of the focus of a research project, the fact that mathematics is a human practice means it is inherently political, rife with issues of domination and power, just like any other human practice." (Gutiérrez, p. 40)

My 2012 looked similar to my 2011 - a lot of reading, writing, studying, and teaching. Throw in a bunch of running and a pretty miserable Cubs season and the year came and went pretty quickly. I traveled back to Iowa for the first time in four years, giving me a chance to visit old friends and help my parents a bit. However, if my 2012 is highlighted by anything, I think it comes down to three things: experiencing some great speakers here at CU-Boulder, passing my comprehensive exams, and not only setting, but reaching, a running goal.

Great Speakers

Comprehensive Exams

Running

Best of 2012

After a summer of running and a couple trips to Rocky Mountain National Park, I felt like I was ready to climb Mt. Meeker. I didn't want to climb it alone, but luckily one of our new doctoral students, Elizabeth Schlessman, wanted to climb Meeker, too. Knowing the peak of fall weather was at hand, we set out on a beautiful Saturday to see if we could summit Longs's nearest neighbor.

Elizabeth and I hit the trail around 6:30 and steadily moved above the trees and got the classic view of Meeker and Longs. This is really a wonderful place, and getting there was far easier than I remembered it from my climb of Longs in 2000. Then again, this time I was in shape, accustomed to the altitude, and not carrying 45 pounds of camping gear.

Coming into the Olympics, I had a hunch that these games were going to be remembered for the performances of the U.S. women. Maybe it had something to do with the local media attention on Missy Franklin, or my native state's attention on Gabby Douglas and Lolo Jones, but it seemed there was a lot more talk about our female Olympians than there was for the men. (Michael Phelps is the obvious exception. Remember, NBC thought it was worth skipping part of the Opening Ceremony so we could listen to Ryan Seacrest ask him about his fear of spiders.)

Now through 13 days of competition, it appears my hunch was right. U.S. women have so far won 51 medals to the men's 38 (neither figure counting the bronze won in tennis mixed doubles), and the women have struck gold twice as often as the men, 26 to 13. Give yourself this quiz: Name a male U.S. Olympic gold medalist who isn't a swimmer. (crickets) Give up? It's not easy, because there have only been three: Vincent Hancock in shooting, Christian Taylor in the triple jump, and Ashton Eaton in the decathlon.

(Side note: How backwards is it that we give so much more hype to the "World's Fastest Man" instead of the "World's Greatest Athlete?" Do we just lack the patience to follow the decathlon competition?)

Now, I know the games aren't over yet, but I find this imbalance pretty astounding. Yes, there have been some hard-to-explain surprises for the U.S. men: Zero medals in boxing for the first time ever; Zero medals in Greco-Roman wrestling, the first time that's happened since 1976; and no American men in the 400m finals, an event we've won the last seven Olympics, sweeping the medals in 2008, 2004, and 1988. Maybe these are just flukes, an unfortunate accumulation of bad luck. But I don't think the performance of the women has much to do with luck. I think a lot of credit should go to Title IX (despite what effects it may have had on minor men's sports), which just recently celebrated its 40th anniversary. This country opened up opportunities for women to participate and compete, and they've flourished. We should be proud of this as a nation, and we should be proud of these women as individuals.

I've loved watching the U.S. women compete in these games. The women's indoor volleyball team has been excellent and I even stretched my soccer tolerance to 10 whole minutes to catch the end of the gold medal match we won against Japan. I was especially happy to see Allyson Felix win a gold in the 200m after silvers in the past two Olympics. But do you know who I looked forward to watching most? Two wrestlers: Clarissa Chun and Ali Bernard, both returning Olympians from the Beijing games. You've probably never heard of them. In a way, that's what makes the Olympics great -- you discover some athlete who has been toiling day-in and day-out with little reward or recognition, just waiting to be discovered by a national audience. Being a wrestling fan, these two women aren't as obscure to me as they are to most people. I've known about Clarissa since she won a World Championship in 2008, and I really had hoped to meet her when I was coaching and we took our state qualifiers to workout with the women's freestyle wrestlers from the Olympic Training Center. (She wasn't there, sadly.) Clarissa won a bronze medal in London by beating a long-time Ukrainian nemisis, and if there's a tragedy in these games, it's that Clarissa broke her phone during the opening ceremonies. (Who do you think took the photo of teammate Elena Pirozhkova lifting Michelle Obama?)

I really didn't know much about Ali Bernard before the games, but as I watched matches and interviews on YouTube before the start of competition there was something special about her that drew me in. Maybe it's because I can imagine what it was like for her to grow up in rural Minnesota, and the challenges she faced being a girl in a predominantly boy's sport. Maybe it was imagining the big step she took to leave the U.S. and go to college in Canada where there was a women's wrestling program, or the sacrifice of committing herself to the training required for world-level competition. Maybe I can imagine her ups and downs the past year: a bronze at the 2011 World Championship; being named Women's Wrestler of the year; losing at the Olympic Trials despite being the favorite; having ankle surgery; then making the Olympic team after the original qualifying wrestler failed a drug test. You'll have to pardon me, Kobe and LeBron, but Ali Bernard's journey to the Olympics satisfies me in a way yours does not. And Ali's result is, to me, no less Olympian: a hard-fought first round loss, a dream over in four minutes as her hometown watched and cheered her on. As did I.

As much as I've enjoyed pinning my hopes to Ali, I could have been cheering for anyone. With a few different clicks on YouTube, maybe I'd have been getting up at 6am to watch a heptathlete, or a rower, or a boxer like Claressa Shields, the 17-year-old from Flint, Michigan, who won a gold for the U.S. The U.S. seems to have so many talented female athletes to support, and many of them have knocked-down-get-up-again histories like Ali Bernard. They're everything we expect our Olympians to be, and often times more. Winning so many medals is just icing on the cake.

Unfortunately, it hasn't been a perfect Olympics for the U.S. women, or at least our perception and judgement of them. Being a successful female athlete in America still has its problems. First and foremost, I could happily do without linkbait like "20 Hottest Olympians of London 2012," to which I won't give any extra traffic by linking to here. Even NBC (and my local NBC affiliate) shamelessly published such an article, complete with plenty of bikini and semi-nude photos of female Olympians. I don't have all the answers here, but somehow our culture just hasn't quite figured out how to recognize their fitness and attractiveness -- which they should be free to display, and we should be free to appreciate -- in a way that I think is appropriate and not gender-biased. (The worst example: One site posted pictures without the names of the athletes or other identifiers. Just pictures.)

It was also disappointing to see some of our biases and double-standards get targeted at individuals. For example, in the midst of Gabby Douglas's run at all-around gymnastics gold, the internet buzzed with criticisms of her hair. And the biggest drama of the games might be that surrounding Lolo Jones, which she referred to in this Today Show interview:

After a month or so spent getting my running legs solidly underneath me, I figured it was finally time to head west into the mountains and climb something. After looking at destinations relatively close to Boulder, I chose St. Vrain Mountain, a peak located on the border of Rocky Mountain National Park and the Indian Peaks Wilderness.

I'm sitting myself down tonight after a long baseball season to watch the Cubs for the final time this year. After Ron Santo died last winter, this season I decided to upgrade myself from MLB.com's Gameday Audio to the full MLB.tv package so I'd have access to every Cubs TV broadcast this year. I watched every one. I might not have watched them live, and for quite a number the game became background noise as I worked on something else, but in one way or another I've watched every single game this season. It's not quite like getting season tickets and attending every home game, or like visiting all 30 major league ballparks, but it's something.

And why Google+ won't be replacing Twitter or Facebook for most of us anytime soon

Tomorrow I begin my second year in the doctoral program in the School of Education at the University of Colorado at Boulder. Being a doctoral student isn't quite like being a student at any other level. Doctoral work is more of an apprenticeship, although there are plenty of classes to attend and papers to write. I imagine there are a number of qualities our faculty look for in us doctoral students. During our first year, they see if we can grasp the fundamental methods of quantitative and qualitative research, and they test our understanding of the major political and philosophical issues in our field. During our third year, we'll take a comprehensive exam to measure if we have the focused expertise and vision necessary to go on to pursue work towards a dissertation that will contribute new knowledge to the field. So what do they look for in our second year? If my schedule is any indication, they must be seeing if we can maintain our sanity despite heavy workloads. I hope I'm up to the task.

The typical full course load for doctoral students is three classes (nine credit hours). To an undergraduate that sounds like an unimaginably light load, but the work is different at the doctoral level. This semester I'm taking the last of my core courses, Multicultural Education, as well as two other courses: Advanced Topics in Mathematics Education and Measurement in Survey Research. All will keep me busy.

In addition to our courses, most doctoral students beyond their first year have a 50% assistantship, meaning the work is expected to take 20 hours per week. When I came to CU, I expressed a desire to teach. Last year my appointment was a research asssistantship. I was a bit jealous of my colleagues who got to work with students, but I immensely enjoyed working with my advisor on some of his research projects. This year, however, I don't just get to teach a class, I get to teach four classes. I never thought I'd be teaching more classes than I'd be taking, and for all I know a four-class teaching load is some kind of grad student record.

The courses I'll be teaching break down like this: Three are for math and science majors who have expressed a interest in teaching, and those classes meet once per week for an hour and fifteen minutes each. In addition, those courses are co-taught and we have all the materials (lesson plans, activities, handouts, etc.) from past semesters at our disposal. My fourth class, however, is a totally different ballgame. I'll also be teaching basic statistics to undergraduates. That class meets once weekly for two and a half hours per meeting and I'm pretty much on my own when it comes to lesson planning and activities. Normally they'd give that class to a more senior grad student with experience as a teaching assistant, but this year they're taking a chance on me to do the job. Fortunately, I've got some great people around me who can offer advice and support, and if I'm smart I'll take all of it I can get.

We tend to get a lot of sunny days here along Colorado's Front Range, but right now we're enjoying some much-needed rain. After a couple rainy days earlier this week, the clouds broke Friday morning and we got one clear day before the clouds and rain returned today. Anticipating a nice scene when the clouds broke, I set my Kodak Zi8 on a tripod in my window and let it run. I cut out a 15-minute piece of video using Avidemux and then used modified code found here and here to prepare the video. First, I extracted two frames from each second of video:

I really don't get excited about the coming and going of school years. In fact, the end of a spring semester always makes me a bit sad. Teachers and students are working at their peak (or their limit), showing off all that they've learned and accomplished and then it just stops and suddenly it's summer. My transition into summer will be smooth, as I'm still working for my advisor and I'll be taking at least one class in July. But I suppose getting this far is an accomplishment in itself. I don't know how much longer it will take for me to finish my doctoral program, but I know I'm now one year closer.

Now that we first-year students have some breathing room, my friend Jackie and I headed out yesterday for a photography excursion. Our destination was Red Rocks Park and Amphitheater, located west of Denver near Morrison at the edge of the Rocky Mountain foothills. Red Rocks is, by almost all accounts, the best natural amphitheater in the country, if not one of the best in the world.

I'm pretty thorough about backing up my data. Here's my typical routine:

1. Any school-related files are in Dropbox, so they're available everywhere and backed up.
2. A rsync script cron job makes a new "snapshot" of all my data to an internal 2TB drive inside my computer. The script runs every 8 hours and keeps the 3 most recent snapshots.
3. The same rsync script run manually copies to an external, encrypted 2TB drive that I take to my office.

My friend Jordan and I went down to the Air Force Academy today to watch some Division I wrestling action at the West Regional. I went to support my UNI Panthers and, judging by the results, my support wasn't enough. UNI came in second behind Wyoming and UNI only had two champions, Ryan Loder and Christian Brantley. Loder's final over Wyoming's Joe LeBlanc was quite good, with Loder avenging a loss two weeks ago by controlling LeBlanc from the top position in the third period. It was a good match between two very evenly-matched wrestlers.

My biggest disappointment came in Brett Robbins' true second match against UNC's Justin Gaethje at 149. Robbins upset Gaethje in the dual last month, and ever since I've been a proud member of the Brett Robbins fan club. Today's rematch was close and the score was tied 4-4 with about 10 seconds left when Robbins was penalized for stalling, giving a 5-4 victory to Gaethje. I don't often dispute an official's call, but this one was horrible, particularly given the circumstances. Coach Schwab was absolutely livid.

It looks like UNI will only have 3 NCAA qualifiers this year: Loder, Brantley, and David Bonin. Jordan and I wrapped up a long day of wrestling the best way we know how, with a buffet-full of sometimes sketchy food at the GC.

When your engineers have 20% of their time to use on projects of their choosing, you get a lot of interesting product ideas. If nothing else, Google is amazingly unshy about pushing these products and services to their users, even if some start out somewhat incomplete and poorly integrated. Enter Google's newest offering, Google Buzz. Unlike some previous Google attempts at social media, this one is going to work in a big way.

First, Google integrated Buzz right into Gmail, the reason most of us have Google accounts in the first place. There are plenty of seats at the Google Labs table, but not many projects get to sit at the front with Gmail. Second, your contact list pre-establishes a social network. Third, if you use Google Profile, you already had established information about yourself and the content you create. Fourth, if you create content with Blogger or Reader, your Buzz account is pre-primed with content. Who else could have done this? Nobody. (Even though Buzz is more like FriendFeed than anything else, Buzz will succeed where FriendFeed didn't because of these things I've just mentioned. Honestly, though, life might have been easier if the world would have just used FriendFeed from the beginning and forgotten about Twitter and Facebook.)

Posting content is easier than ever, and (thankfully!) sharing that content between services is relatively easy. I can post to Twitter and my tweet automatically shows up in Facebook, FriendFeed, and Buzz. I can take upload a picture from my phone and Flickr automatically sends a tweet, spreading the photo everywhere. (Unfortunately, Facebook, FriendFeed, and now Buzz also monitor Flickr separately, so that photo comes twice.) Social networks almost appear effortless, except for one major thing: COMMENTS.

The interaction of users and content is what makes this social media, but with every new service that interaction gets increasingly fractured. Let's look at my last scenario: posting a picture from my phone to Flickr. If you want to make a comment about that picture, where should you put it? Let's count the choices:

1. You can comment on Flickr.
2. You can reply to the tweet generated by Flickr.
3. You can comment on the photo on Facebook (which pulls the photo from Flickr).
4. You can comment on the Flickr-generated tweet on Facebook (which pulls the tweet from Twitter).
5. You can comment on the photo on FriendFeed (which pulls the photo from Flickr).
6. You can comment on the Flickr-generated tweet on FriendFeed (which pulls the tweet from Twitter).
7. You can comment on the photo on Buzz (which pulls the photo from Flickr).
8. You can comment on the Flickr-generated tweet on Buzz (which pulls the tweet from Twitter).

It's not difficult to find Iowans in Colorado. We're everywhere. Even more, I'm sure more Iowans are getting ready to move to Colorado right now. As an Iowan-turned-Coloradoan myself, I thought I should provide this translation guide.

I've always been a fan of Wikipedia, and often I'm happy to see a Wikipedia entry as my top search result. As a math teacher, I never had many opportunities to direct students in the ways of research, including how to choose appropriate sources. Several of my colleagues who do teach research, however, not only discouraged Wikipedia use, but banned it outright. Why? The most common answer: "Because anybody can edit Wikipedia, students won't know if the information is true." It wasn't until tonight that I saw how shortsighted this reasoning really is, and how it gives students wrong ideas about research.

At its very core, linking websites together is what makes the web the web. I've had my own website since 1996, and like many people, we all had a page dedicated to our favorite links. In 2001, my friend Brian Gongol (and he certainly wasn't alone) went a step further and provided not just a list of links, but rather a stream of updates, whether they be sites of interest or news of the day, each complete with Gongol's thoughtful commentary.

It's back to school time again, and this year I'll be returning as a student instead of a teacher. While the decision seemed sudden, this has been in the works ever since I left UNI. I was so influenced there by Dr. Bonnie Litwiller, my academic advisor, and Dr. Ed Rathmell, my thesis advisor, that I knew someday I'd want to go to graduate school and pursue higher degrees in math education. But first, for reasons of experience and credibility, I went to Colorado to teach, learn, and explore.