How can you help your kids in math?

I ran across this post today at The Educators Room, titled It Starts at Home: How Parents Can Help Their High School Students in Advanced Mathematics. I like essay overall — it speaks to parents who may not have been comfortable with math when they were in school, and gives them some ideas about how they can help their children without having to become math experts. I particularly like what the author relates about his mother, who supported him in math even though she felt that she was “bad at it.” These days, I know we discourage parents from saying “I’m not really good at math” to their kids, but I also think it’s important that we don’t lie to our children. It’s OK to let our kids see us struggle — they can learn perseverance and see us not simply giving up because we are “bad” at something. So let your kid know that math has been tough for you, and then listen to them while they explain some math to you, and really try to understand what they say. It will do your child a world of good to see you trying and learning. I also like that the author of the article reminds parents that there are a lot of different skills needed in math.

Mostly, this essay reminds me that I’d really like to write my own “how to help your child in math” essay, so perhaps this is the poke that I need to move forward on that!

Classroom poster with students names and mastered math facts

Shame in classrooms

I ran across a blog post by Brené Brown earlier today. In the post she relates some of the kurfluffle around her comments to Oprah Winfrey about teachers and shame (original video now hard to find — its the last clip on this page). This all happened at the end of September, so I’m late to the party, but I had a few thoughts about what happened here . To my mind, the biggest place where Brown goes wrong is when she says that shame is a classroom management tool used in schools. By calling shame a tool, she implied that the use of shame was conscious, and since her whole thing is talking about how bad shame is, that’s a pretty damning way to call teachers out as being bad for kids. That turned her comments into a public shaming of teachers. Brown didn’t intend to shame teachers, but that’s the sneaky way shame works — it’s everywhere, and it is hard to avoid.

Shame is certainly present in every classroom — it is a nearly ubiquitous emotion, so it happens in classrooms like it happens everywhere. For the moment, let’s try to avoid shaming the emotion of shame — shame and the threat of shame are intertwined with nearly every connection we have with other people. That’s not good or bad, it just is. When our relationships are working, we are able to use subtle clues about shame in ourselves and others to figure out how to navigate the relationships without alienating ourselves or other people. But an excessive weight of shame, or shame that calcifies in certain areas can break our relationships, causing disconnection and isolation. In classrooms, both students and teachers can feel shame, and that shame is a signal to us that our relationships are either fractured, or in danger of being fractured. Teachers feel it when they are disrespected by parents, administrators, and other teachers. Students feel it when they understand that they aren’t worthy of connection with classmates, teachers, and specialist because they aren’t good enough. We have to watch for signs of shame in other people, and use it as a sign of relationship danger. Relationships can be repaired and shame can be healed.

Teachers care about kids, that’s why they become teachers. They work hard every day to help kids succeed. They also face a job that is so difficult, so painful, so demanding of every resource they have. They do it without enough pay, and with a whole world watching to see where they are going to screw up first. In other words, teachers do their jobs in an environment that is a shame pressure cooker. When people are in that kind of pressure cooker, they will push their shame onto other people, and it is easiest to push shame onto weaker people. I do it as a teacher to my students, and I do it as a parent to my kids. I don’t do it because I’m a bad person, or because I am sitting around cackling and thinking up ways to torture students and children. I do it because I am human, and fallible, and, because, as Brown said in her mea culpa post “learning is vulnerable and classrooms are tender places.” We do need to raise awareness of the presence of shame in classrooms because awareness is really one of the only ways to combat shame. But we have to raise that awareness gently and carefully because any time we start to really see how shame operates in our lives it is easy to become overwhelmed.

I do think there are some institutional practices that increase students vulnerability to shame in schools. Particularly, I am thinking about public accountability in classrooms. In elementary math classes, you will sometimes find charts of times tables and other math facts, where you can see how each student is doing on proving their mastery. Short timed tests like “mad minute” are used in most elementary classrooms, and those are also a form of public accountability since all the students know who finishes on time and who doesn’t because they can look around and see everyone, including those kids that inevitably shouted out as soon as they were finished, before the timer rang, stopping the kid who still had half a page of problems left. Public accountability charts are also used for behavior management and in other subjects. For some kids, this is highly motivating. Students want to do well and the competitive spin of public results help spur them to work. But for other students, being at the bottom (or even in the middle) week after week is demoralizing and shaming. I think that in order to support all students, we need to have students set goals and chart their progress, but that this should be private. This won’t provide the competition that helps some students focus, but it will avoid the discouragement and feelings of shame and stupidity that other students experience.

Classroom poster with students names and mastered math facts

Here not only is your math prowess public, but it’s linked to ice cream

We can’t change the fact that in every classroom, the students know where they stand in academic rankings. All of the students know who is at the highest reading level and who is still struggling to read beginning books. They all know who finishes the math assignments before everyone else and who never finishes. We humans are constantly comparing ourselves to others, and figuring out where and how we rank. But when those rankings are publicly displayed, their importance is reinforced, even if the teacher is telling the students verbally that effort and progress are the most important things. We need to put the rankings away and to consistently remind students that they need to look to themselves to measure progress. They need to be better able to handle fractions at the end of the unit than they were at the beginning. They don’t need to be better than another student, they need to be better than they used to be. We also need to talk to students about how we handle that terrible feeling we have when we realize that we aren’t doing as well at something as we wish we were. We need to talk with our kids about how to manage the pain when we find out we sang the wrong note, or messed up all the problems, or our drawing wasn’t selected for the prize, or we realize that our friends are all reading at a higher grade level than we are. If we avoid emphasizing rankings and do some explicit teaching around how to handle the emotions that arise when we fail or don’t do as well as we would like, then we give students the tools to navigate pressure and criticism without falling into a pit of shame. Most teachers already do a lot of work to combat shame, but connecting the dots on the impact and mechanisms of shame can help teachers better see what they are doing and how to do it effectively.

Our successful schools

School closings rally

School closings rally (Photo credit: chicagopublicmedia)

I have been thinking a lot lately about the failure of our schools, particularly with regard to mathematics. It’s impossible not to notice what a terrible job our schools and students are doing at math, particularly when I am reminded about it once every hour or so by my twitter feed. I got on this kick because of the latest way we’ve been flogging ourselves, the PISA (Programme for International Student Assessment) results. When you look at the US in the rankings of countries, you won’t believe where we stood. We were, well, average. I know that here in the US we think that we live in Lake Woebegon where everyone is above average, but being average is just, well, average. The sky isn’t falling and our scores didn’t drop alarmingly. We’re all OK.

What if we aren’t all terrible at math, and what if our schools aren’t letting our students down? What if our schools are doing an OK job of educating students? Are they doing the best job possible with each individual student? Not likely. Are they moving lots of students through the pipeline, teaching them to read, do math, write, understand politics, know something about history, and even giving them a little art, music, and physical education? Yes, we are doing all that and more.

Remember the 90s and how Baby Eistein and similar products brought us the mistaken idea that if it is good to parent your kids, then its even better to parent them really really really well? If parents do flashcards, teach their babies to sign, buy the right educational toys, and twist themselves into the right knots, we will raise a generation of kids that is uniquely poised to become super-geniuses. Except that none of it really works. Yes, when a child is hungry or neglected, or when a family is living too close to the edge to provide a normal environment for the child, then the child’s brain will be impacted in a negative way. Poverty really does hurt kids. But that doesn’t mean that environments that are excessively enriched will produce geniuses. More is better when you don’t have enough. But when you do have enough, more won’t continue to produce improvements in results.

The same is true of schools, of math education. We need to have schools that are good enough. Schools should be full of teachers that care about kids, that have some training in both subject areas and pedagogy. Schools should have the financial resources and leadership to support teachers and families. But schools don’t need some kind of huge overhaul. There is no magic bullet of ipads or entrepreneurship that is going to change our failing schools into amazingly successful schools. Sometimes it seems like we have found the answer. Like giving kids computers. Like unschooling or hackschooling. Like teaching kids to code. There are a lot of good ideas out there, but we can do them all and still not get better results. That’s because our schools are already doing OK, and thus any new idea we cram into our full educational system will replace something else that was already good for a lot of kids.

Yes, we should continually look to improve the way we educate kids. From where I sit, I see that we should particularly pay attention to how kids learn math, what math they need  to learn, what math they might want to learn, and how to creatively help kids get more of what they need and want while we still have them in this amazing system that seeks to help absolutely everyone to gain skills and knowledge. But we will get a lot farther in that enterprise when we acknowledge that we are trying to solve a problem that is really hard, and that the people who are at the front lines of our educational system — the teachers, support staff, parents, administrators, and higher-education faculty — are doing a lot of amazing things and having a lot of success already.

Math is jarring

I ran across this video yesterday, by a math major, taking about other people’s reactions to learning that she is a math major.

I particularly like the analogy around 1:15 where she is talking about the jarring nature of switching from ordinary conversation to math. She likens it to being asked mid-conversation to compose a poem in Russian when you don’t know Russian. I think that is a lovely analogy. She notes that math feels this way when you are not used to it, and sometimes even when you are used to it.

I think this is an apt analogy, because academic math comes out of left field for most people. In math class, it isn’t that weird to have someone tell you:

The track at Made Up School is one mile long and features semi-circular ends connected by straight lines. Find the area enclosed by the track as a function of the radius of the semicircles. What dimensions allow the maximum area to be enclosed by such a track?

Say what? What does it look like? If the track is there already, how can we change it? Why are we doing this? And sometimes things get even worse:

If line segment BD is a perpendicular bisector of line segment AC, prove that triangle ABC is isosceles.

It just makes your brain hurt due to the sheer number of technical terms, and I have no sense whatsoever of this being a meaningful task that there would be a human reason for being able to do.

Notice that this is very different from other subjects that we study in school. In history, you might be asked:

In 1938, British Prime Minister Neville Chamberlain chose to adopt a policy of appeasement toward Hitler’s aggression against Czechoslovakia. What did this mean? (from this list of sample questions)

There may be some confusing terms in here. Maybe I’m not totally sure what a Prime Minister is, or who Chamberlain was, or where Czechoslovakia was in 1938, but I can get the sense of the question and have some idea of why I might want to be able to answer it, namely because I want to understand how the international world works.

Same with a thick subject like physics:

A battery is connected to a light bulb with copper wire to complete a circuit. The bulb immediately lights. Why?

Whoa, that’s intense. You are asking how a battery works. It may seem like a hard thing to understand or explain, but I can see why I would want to try an answer it — because I want to know how the world of electricity works.

I am not suggesting that there is no point to learning “higher” mathematics beyond arithmetic, but I am suggesting that those reasons can be obscure and subtle. We learn mathematics past basic computation because we want to understand the world, but it is an understanding of the world of thought, the world of algorithm, the world of logic, the world of abstraction. It is not the “real world” that we are seeking to understand, although higher mathematics often does have applications in the real world. Instead it is a fantasy world in which we ask “what if” and try to find a way to get consistent results. It is a world that is jarring precisely because it is so headily academic and is tethered to everyday concerns like a balloon that may slip away.

I think that if we all realized that we currently have enough math to understand our worlds, we’d all be a lot happier. The math most of us use in life is more straight-forward than it is portrayed in school, and  you may, right now, be as good at it as you need to be. Or you may find that you have some math-related problems in your real life that always frustrate you. That might be because they are really hard problems, and would be hard even for someone with advanced mathematical training. For instance, if you want to figure out a system of bonuses for your employees that reward certain types of job performance, then you probably will want to use some math, but the problem won’t be simple, and math will only be one part of the solution.

I also love the end of the video above where Sarah emphasizes practice, and the fact that mathematical skills can be developed. Absolutely true. You probably already have most of the math skills that you need, and if you need more, practice is a good way to get more. Of course, one of the big troubles that I see is that K-16 math classes don’t give people skills they will need after school, and it is actually quite hard to find needed and useful math skills if you aren’t in a STEM field (see, for instance, Audrey Watters on the difficulty of learning to code).