Tuesday, April 7, 2020

Working from Home: Physical Setup

Many people are shifting to working from home. As they do, I see lots of people are shifting from working from their couches to setting up make-shift work spaces. Here are some tips that could help:

  1. Consider designing your space so you can stand at your desk periodically. It's a nice change of pace for your back. I have a pretty cheap Ikea desk with a motor that raises and lowers it, but you can also get a Varidesk or use milk crates or something similar.
  2. Get up and walk every hour or so. Do a quick chore or check the mail or something.
  3. Keep hydrated. If you use normal-sized drinking glasses, this can dovetail nicely with #2.
  4. If you start to get pain in your arms or fingers, invest in a wireless curved keyboard. I use a Microsoft Sculpt and love it.
  5. Setup your chair, desk, monitor, etc. so they are ergonomically sound. Mayo Clinic has some advice on office ergonomics
  6. Not everyone can locate their home office in a separate room like I can. Still, you need a space, and you should find a way to physically check in and out of "the office." When I started working from home, my space was in the family room attached to our kitchen. Not ideal, but it's all I could do at the time. To check in and out of the office, I would turn the monitor off. Though I could still check and reply to emails on my phone, having the computer/monitor off helped me set a boundary.

Pay attention to your physical work space. If you don't take care of your body, it will punish you.

Friday, April 3, 2020

Helping Your Kids Keep Learning: Math

As many school districts close for the remainder of the academic year, many parents are struggling with several issues:
  1. If the teacher isn't doing much, what should I have my kid(s) do?
  2. What are some good resources for math curriculum?
  3. What are some good resources for math help?

What Matters Most?

A: Not losing ground. Studies show that students lose a fair amount of ground in the summer. Imagine a summer that lasts 5 months instead of 2.5! Therefore, I really care about progress. Get them to do something that is close to grade-appropriate. I just don't want them to forget how to do math.

B: Being ready. This is tougher to do, but if a student is taking a course now that has foundational content for next year's course, then I care about those foundational skills and concepts. The trick is identifying those key things. Achieve the Core has really helpful Focus documents for each grade. Look for the solid green squares. These are particularly helpful for anyone in a Common Core state. It's not always so easy to identify the key foundation content, so you might need to reach out to a teacher or curriculum person for guidance. One of the important things to keep in mind is that not everything is critical. You don't need to jam it all in there. Pick and choose carefully.

C: Liking math. If your approach to being ready results in a student who hates math, then you've created problem. I know this is tough, but you need to find a way to keep them moving forward that doesn't spoil whatever affinity they have for math. Not losing ground is more important than being ready, and liking math is perhaps most important.

Math Curriculum Resources

If you are pretty much on your own for helping your kid move forward with math, consider going to UnboundEd and/or OpenUp. They have solid content with good focus, rigor, and coherence. Please avoid entering the wild west that is Teachers Pay Teachers. TPT has a ton of issues I won't go into, but suffice it to say that I'm not a fan.

Math Help

What if you or your student gets stuck on some math topic? Note that this is really different need (and set of solutions) from the curriculum focus above.
  1. If you haven't checked Khan Academy, you haven't done a serious search. I would not use this as a curriculum, but the videos can help a learner get over a bump in the road.
  2. BrainPop is another good source of videos. There are a ton of others, and you can find many at OER Commons.
  3. Friends and family could help. Who do you know that is good at math? They are likely sitting at home, and would be happy to help and interact with someone new. Lean on your network!
Progress is important, but don't stress anyone out. The current state of affairs is inherently stressful, and math shouldn't be part of the problem. I hope math can be part of the solution -- doing some math work could fit as part of a new daily structure that provides some semblance of consistency and normalcy. 

Thursday, April 2, 2020

Novel Coronavirus & COVID-19: Data, Models, and Visualizations

This is not intended to be a complete analysis of the current pandemic. Rather, I just want a place to collect some particularly helpful articles and resources.

About the Models

Why It’s So Freaking Hard To Make A Good COVID-19 Model Creating a math model for something as complex as infectious disease is not easy, but COVID-19 is particularly difficult. Fivethirtyeight.com does a nice job of walking through many of the reasons that creating good models for it has been (and continues to be) so challenging.

Don’t Believe the COVID-19 Models -- That’s not what they’re for is The Atlantic's attempt to get people to understand the nature of modeling.

Data Visualizations

Coronavirus Infographic Datapack by Information Is Beautiful is my go-to spot for nice graphs. The first one uses a log scale, and is a great example of when and why log scales are so helpful for making sense of exponential phenomena. Basically, anything that looks like a line is experiencing exponential growth. The steeper the line, the faster the rate of exponential growth.

Coronavirus in the U.S.: Latest Map and Case Count is from the New York Times.

Coronavirus COVID-19 Global Cases at Johns Hopkins' Center for Systems Science and Engineering was the first tool I used to track the virus' spread. I still find it helpful for digging into geographic centers.

The Blog Awakens

As we all come to grips with a new normal, lots of things that seemed really stable have shifted. Working in offices, going to school, hanging out with friends, and grabbing an Americano at my local coffee shop have either been eliminated or drastically changed.

Lots of these changes have pulled many people closer to my daily reality and experience. I've worked from home for several years, develop curriculum for distance learning, and have an active virtual network of friends. I miss getting an Americano and hanging out at my local coffee shop, but less of my life has had to shift than for many people (e.g., my wife and kids).

I'm awakening the blog so I can opine at some length about topics that could possibly be of interest or value to people who are trying to forge a new normal.

Tuesday, April 30, 2019

But Seriously... Is Algebra Necessary?

A friend tagged me in a FB post with a link to a New York Times article by Andrew Hacker Is Algebra Necessary? I need to process this, so here goes....

I saw the article as having two distinct parts. Here are my reactions to each part.

Part The First: Math Is a Useless Pain

The first half or so of the article indicates that math causes high dropout rates and is basically useless to everyone not bound for MIT or Caltech. Well, if math causes high dropout rates, then I think there is a reasonable discussion to be had about how we address the issue. What should we do?
  1. Prepare students more effectively from the beginning. That is, should we fix our elementary and middle school math programs so that students can have more success later in their math careers.
  2. Fix the high school math curriculum so more students can find success and gain the math skills they need for life and for later mathematical study.
  3. Give up. Stop requiring so much math.
The eye-grabbing headline and some of the arguments in this first part seem to imply that Hacker is suggesting a focus on option 3, but after reading the second half of the article, I think he is making more of an argument for option 2. I believe that we need to focus on options 1 and 2.

By the way, the Common Core standards should  help with option 1. A coherent curriculum that focuses on important mathematical practices and covering fewer topics, but with more depth is a great place to start. It isn't a panacea, but spending more time on fewer topics can help everyone out. I think the Common Core standards do a pretty good job of mapping out a coherent mathematical progression from elementary school through the end of grade 8. Then, we come to...

Part the Second: The Traditional Algebra 1-Geometry-Algebra 2 High School Math Sequence Is Mostly Useless and Should Be Improved

OK. This is where Hacker and I agree. In an earlier post, I said that we drive too many kids (like cattle) on the pathway that leads to Calculus. As I said in Math Illiteracy, everyone needs to master some math skills and understand some math concepts, but these don't necessarily map well to the cattle drive to calculus that I think is over-enrolled. By pushing just about every kid through the same cattle drive, we are driving kids away from math and putting up barriers to later pursuits that should not be dependent upon relatively esoteric skills such as learning how to factor cubic polynomials.

Maybe most kids should take a (perhaps more applications-oriented) course in Algebra, but maybe fewer kids need to take geometry and Algebra 2. Maybe a course in Practical Math (the actual title of a course on which I am working) could help. This sort of course can help students see how math can be a tool for solving problems. It can still be a pretty rigorous course, though it certainly wouldn't prepare anyone for calculus. But then again, not everyone needs to take calculus.

From my perspective, the tricky part centers around mobility. If we have a math pathway that prepares potential engineers, scientists, and mathematicians with the math skills they need, and we create a separate pathway that helps the general non-mathy population acquire the skills they need, then how do we ensure that a student who starts on a less rigorous pathway can change his or her mind and switch to the mathy pathway? How do we make sure that the less rigorous pathway doesn't become a dumping ground for students who are ill-prepared for the more rigorous pathway? These are very real concerns. Perhaps I'm being a paranoid Black man, but I know that this sort of dumping ground mentality has been wide-spread in the past, and I'd hate to create a two-tiered curriculum that institutionalizes it.

The Bottom Line

As Hacker says:
Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.
Here, he is talking about how medical schools (and other post-graduate programs) use calculus as a way to identify students who have the right academic stuff. Honestly, I can't see that changing any time soon. Also, I'd be interested in a study about this. Maybe being able to learn calculus has a high correlation with the ability to survive and thrive in medical school. Maybe this extends to undergraduate studies as well. As the author of the A Mind for Madness blog says in Thoughts on Nicholson Baker’s Case Against Algebra II:
... if a high school diploma is meant to indicate some level of readiness for college, then algebra is probably a good indicator. This does not mean that you will use it, but will just point out that you have some ability to do some abstract things. I’m not saying it is the only way to test this, but it is probably a pretty good one.
Regardless, I think we need to:
  • Prepare more students for success in mathematics more effectively. We shouldn't focus solely on the cattle drive to calculus, but then again, we shouldn't ignore it either.
  • Do a better job of creating math courses that engage all students. We need to have students wrestle with more authentic real-world applications and see how math can help solve real problems.
  • Help students see the beauty in math in addition to the utility it affords in problem-solving contexts.

Tuesday, April 23, 2019

The Cattle Drive: Too Much Calculus

Reading Pamela Burdman's piece at Hechinger Report: Numbers evoke joy and wonder, why doesn’t math class? got me thinking.

I have already argued that we push too many kids to Algebra too early. Now to complain about the other extreme.

High school students are often driven like cattle through their math courses. Those who can withstand the cattle drive make it to the fertile pastures of calculus. Sadly, many of the herd don’t make it and are left along the side of the trail.

Not every student belongs in calculus. Though students who plan to be engineers, physicists, mathematicians, or economists need calculus, many others have abilities or interests that make them better suited to other mathematical destinations. The cattle drive hurts kids who lose interest in a destination they don’t care about.

Don't get me wrong: I love calculus. It is beautiful, useful, fun stuff, but it isn't for everyone. Everyone should master Algebra, but not everybody needs to master calculus. And honestly, many of the topics in Algebra II only exist to prepare students for calculus. This doesn't mean creating a dumbed-down track, but maybe there are other options for rigorous pathways.

Why not map out different mathematical pathways for different kids? After Algebra I, maybe some kids would be better served by courses in discrete math, probability, statistics, logic, or some other mathematical topics. Ideally, students would be able to switch back and forth between pathways if enough foundational skills were shared between parallel courses.

I know I'm tilting at windmills, but I'd like to see the cattle drive identify some other destinations; there is lots of interesting, useful math out there. Too many people think they hate math because they hated the cattle drive they were on in high school.

Tuesday, April 16, 2019

Early Algebra: Crushing Kids

Some states want to get all their students to take Algebra by the end of grade 8. The idea is that this will provide equal access to challenging curricula.

The Washington Post's Jay Matthews discussed the issue in Recalculating The 8th-Grade Algebra Rush and the original report is available here: The Misplaced Math Student: Lost in Eighth-Grade Algebra.

I'm a fan of Algebra and a fan of helping as many students as possible master it, but I am not a fan of aggressive time lines for when it has to get done. Pushing all 8th or even 9th graders into Algebra is a problem. Kids who are not ready for Algebra would be better served by shoring up their math foundations. They need number sense, especially when it comes to decimals and fractions. Students who are pushed into Algebra before they are ready are doomed to fail and are probably doomed to hate math forever. I don't want them to take silly math classes that lack any rigor, but I don't want to throw them into classes for which they are not prepared.

At the other end of the spectrum, there is also a push to get good math students to take Algebra in seventh grade or even earlier. Not every kid is ready for Algebra in eighth grade. Very, very few kids should be taking Algebra before eighth grade. If a kid is that good at math, why not provide a more rich mathematical curriculum for the kid instead of just having them rip through the same old courses more quickly?

As you might imagine, my reaction to the title of Jill Barshay's article in the Hechinger Report: Gifted classes may not help talented students move ahead faster was a resounding "good!"

Some of my issues with the "hurry up and go fast" approach to gifted math education:

  1. I have heard SO many stories of kids who took Algebra in seventh grade and ended up losing interest before their senior year. This is anecdotal, so I need to find solid data.
  2. There is solid evidence to support the existence of the Protege Effect: Students who teach their peers deepen their own understanding of skills and concepts. Many parents of precocious students complain that their kids are being held back and doing the teacher's work, but those peer teaching experiences are deepening both students' knowledge.
  3. Teachers at every level complain about students who have zoomed through prerequisites without really understanding everything they need to understand to prepare for later study. For almost all students, that zoom through leaves gaps.
  4. Emphasizing extrinsic outcomes can quash student motivation and long-term interest. Being accelerated can be one of those extrinsic outcomes that push students for a while at the cost of  their own intrinsic motivations to learn.

As Barshay indicates:
"... Research points to the lack of consensus on what the goals of gifted education should be. Many don’t think it should be about advancing students as quickly as possible. High quality instruction that helps kids who’ve already mastered the basics go deeper into the material may ultimately be beneficial. And annual state assessments may not do a good job of measuring this kind of depth, creativity or critical thinking."
Algebra is a good thing. I value its abstraction and generalization and problem solving, but let's make sure that the kids who take it have the right foundation and that it really drives deep learning and affection for math.

Working from Home: Physical Setup

Many people are shifting to working from home. As they do, I see lots of people are shifting from working from their couches to setting up m...