PiCademy

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally Posted July 29, 2017. 

PiCademy

This last weekend I had the wonderful opportunity of attending Picademy in Ann Arbor, Michigan. Picademy is a two day professional development workshop that teaches teachers how to unlock the capabilities of the Raspberry Pi single board computer.

While I’ve been using the Raspberry Pi for quite a while now, I’ve never been able to make the leap to physical computing. I’ve always wanted to be able to make robots and play with sensors and other gadgets that I knew the Pi was capable of doing, but I never knew how. In the past I taught programming in a very dry way. I expect my teaching to be very different this year from previous years. Students will be more focused on what they can make with programming instead of doing assignments in programming.
I’m really looking forward to this year and seeing what my students will accomplish.

If you’re in the giving mood, please help make sure my students have the materials they need to succeed. Donations of any size will help my students, and right now any contribution you make will be doubled by Tom’s of Maine. https://www.donorschoose.org/project/stem-physical-computing-with-raspberry-p/2664110/

What is Standardization?

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally Posted January 4, 2017.

What is Standardization?

During my break I’ve been thinking about the nature of school. I’ve read a lot of articles and I see a lot of posts on social media about the nature of education. The basic gist is that everybody is unique, therefore standardization is bad. This is a bit of an oversimplification, but, generally speaking, I think it’s a true statement.

There is no shoe that fit all learners. Have plenty of the most common sizes, but don’t be afraid to order new ones. pic.twitter.com/AvC5VOe119

— #TeacherGoals (@teachergoals) December 28, 2015

Before the 1800’s Education was not free. Only elite families were able to pay for their children to attend schooling. So, in centuries past if you were a farmer, then your children were certainly also going to be farmers. The occupation of the parent was the future occupation of the child. Education was the job of the parents to impart onto their children, and only education pertinent to the occupation was going to be transmitted. Now this was not a very good system because it removed a great deal of free choice from the children since they could not choose their own occupation.
Enter public schooling:

Education was now something that was accessible (and required) to everyone; not just the elites. It’s true that students in those early public classrooms were not worried about Common Core but there was still a standardization in the classroom. There was a basic 3rd grade curriculum which differed from the basic 4th grade curriculum. Even in the workplace, when you get a new job there are certain policies and procedures that you’re expected to conform to. Even in the days prior to public schooling, the child who was destined to be a farmer was taught the “right way” to farm by his parents. Basically what I’m getting at is that everywhere there is some sort of standardization whether it be in school or home or the workplace.

So I’ll leave off with some open questions. Where do we draw the line? At what point is education too standardized? What is considered the right amount of standardization?
Leave a comment below.

Standardization

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally Posted February 22, 2016.

Standardization

I’ve had a lot on my mind to post about. I’ve just been too busy to actually post anything. A lot of exciting things are happening right now. However, I wanted to discuss a little bit of the opposite of that.

I just finished the Resident Educator Summative Assessment, or RESA for short (I love how this stupid buzzword “summative” still gets caught by my spell check).  In Ohio newly licensed teachers are required to go through a residency program. During this time the “resident educator” is paired up with a mentor teacher who helps guide the new and inexperienced teacher.

It’s a great idea… except it doesn’t work. The Ohio Department of Education is a bureaucracy. Therefore, in place of having a guiding figure to help and support new teachers, they get a standardized “test”. While it’s not a test per se, it’s the closest equivalent there is to having a teacher take a Common Core test. We’re required to record our classrooms, reflect on the lessons taught in the recording, submit evidence about our marking, and submit evidence that we communicate with parents, among other things. This, of course, is without any sort of feedback– which is quite hypocritical to say the least.

There is no evidence submitted, however, that a mentor has actually helped me out. In fact, in the 3 years I’ve been doing this, I’ve met my 3 different mentors only a handful of times (one of them I don’t want to ever meet again).
I’m not really complaining about all the work that I have to do (well I am, but it’s not the main point), I’m complaining about the system. This “system” that has been plaguing students and parents since NCLB was passed- the system which is only getting worse with Common Core- is now creeping its way up to assessing the teachers too. This “Summative Assessment” (seriously try spell checking it!) is just another hoop to jump through that doesn’t truly assess the quality of the educator.

Going through this process has made me wonder what’s next. Will something else come up in the future that will require even more of me and my peers? I don’t know, but I’ve seen people get dissuaded from the profession because of RESA, and although I don’t see myself actually leaving the profession anytime soon, I can’t deny that RESA has made me think about it.

Critical Thinking

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally Posted January 25, 2016.

Critical Thinking

Well here I am, still waiting for my computer lab pieces to come in. I’ve been having meetings with a lot of different people who are all giving me really great ideas on how to create this custom class exactly the way I want, but alas, here I am still teaching pencil to paper.
Perhaps it’s my own impatience, but my students’ questions have started to become my own, and I’m beginning to ask myself “what is the point of this.”
For most of us, the way that we do mathematics in the classroom is not the way we use mathematics in the real world. It’s cool how we can create an equation for pretty much anything, but that’s not how most of us approach it in real life. As a commenter correctly pointed out in a recent post, logarithms are used in every day life when we say things like “I make six figures.” While that may be true, I can’t legitimized a whole unit on logarithms– the meaning, properties, change of base, logarithmic equations– based on the fact that “I make six figures”.

The truth is that I’ve had misconception about my job, as I think a lot of educators do. I’m not a math teacher so that I can teach mathematics; I’m a math teacher to teach critical thinking skills. Actually, no teacher teaches in order to impart random facts onto students that the government deems important for them to know. All teachers, no matter their content, teach for the sake of imparting critical thinking, a love for learning, and method for communicating what they’ve learned. After all remembering is the lowest rank of Bloom’s Taxonomy.

As a math teacher I think my job is made difficult because mathematics is so hard to relate to the real world in meaningful ways, as opposed to some contrived word problem. Even if math is taught in a pure math type of way, many students don’t have the type of minds to be able to appreciate that.
This is why I’ve been obsessing over computer science lately. I think I’ve finally found a way to engage students the logical problem solving. We’ll see how it goes!

Performing Vs. Learning

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally Posted January 7, 2016.

Performing vs. Learning

I’ve been thinking a lot about the difference between performing versus learning. This seems to come up more in math than other subjects due to the obscure nature of mathematics– we always need to legitimize why students need to learn it. That’s its own conversation.


Performing is students completing a task correctly in a timely manner. Performing makes “teaching” easier. Tests and homework can be graded– we can score the student on how she has performed by giving her a letter grade. This is a metric that we have been using for decades to show what a student knows. However, everybody has had their easy teachers and their hard teachers, whether in math or in some other subject. Because of this there is an inherent problem with assessing students with this metric. Different students may have different grades for doing the same work.

Posing an equal and opposite problem is standardized testing. Students are taught to perform tasks, mathematical or otherwise, and get the correct answers. It is, for the most part, procedural thinking. The Common Core was intended to do away with this procedural method of thinking and have students actually learn instead of doing meaningless procedures. Due to the nature of The Common Core being standardized and the requirement to assess millions of students on their progress, students now need to jump through hoops by doing procedures that are more meaningless than they were in the first place.
Learning is much different than performing, especially with mathematics. We teach math that it’s about getting the correct answers, but it really shouldn’t be. The end goal should be that students get the correct answers, but the correct answers should be based on a learning experience that expands their thinking– there are a lot of methods of obtaining the correct answers.
What methods do we use to make sure that students are learning instead of just performing? I’ve got some ideas, but I’ll save them for later. Make sure you’ve seen my previous post: Thoughts from Winter Break.

Thoughts from Winter Break

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally Posted December 31, 2015.

 Thoughts from Winter Break

I've been doing a lot of thinking about the way I want my class to operate. For a long time now I’ve wanted to move away from the classical model of lecturing, practicing, and testing. It’s been a rough ride for me because I’ve been at 4 different schools in as many years. However, this year I have a school with excellent resources and a very supportive administration. I also expect to stay.
One thing I tell my students as they’re learning the math I’m teaching (and I’ve mentioned on this website time and time again) is that they’re not necessarily learning to be able to use math in everyday life (unless you’re a mathematician when was the last time you used a logarithm?), because they may not ever use i after the SAT and ACT. Rather, the reason they’re learning is to make connections and structure their thinking. While that works for some students it doesn’t for others.

We also live in a day in age of high stakes testing. A frustrating reality that my colleagues and I have is a lack of student curiosity– students are only concerned with getting correct answers. I can’t speak for other subjects, but an outcome of this attitude in my class is that many students can’t/won’t work unless the mathematics is procedural. Open ended thinking is something they refuse to do.
Now I could just blame the students, or I could blame that many of them are being raised in poverty, or I could blame the testing culture in which we’re raising them, but that would do no good. That’s all out of my control.
This is why I want to change my approach.

Mathematics is a real art/science that was created to solve real problems. The quadratic formula was originated (though not in its final form the way we know it) by the Ancient Babylonians (I think) to measure the areas of L-shaped fields. That’s nice. That’s neat. I can appreciate that. That makes me want to learn more. But that doesn’t usually intrigue my students. They live in the digital age! Why not use technology to drive learning? I don’t mean using technology as a toy on which they happen to learn. I mean actually learn the mathematics of the technology that they’re using.
Computer science is a field that was mostly established by mathematicians, and my school is a project based school. Let the students learn math through technological projects. With the help of pre-established curricula, like code_by_math(), Bootstrap, Code.org, and Khan Academy, I aim to develop my own curriculum that marries mathematics and computer science. Perhaps this will help students get through logarithms a little easier.

TLDR: Make mathematics relevant to the learner.

What's the point of this? (part 2)

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally posted October 30, 2014.

What's the point of this (part 2)

My last post was about the 3 reasons I thought it was important to learn math in school, even though students may not (probably won’t) use it in everyday life. The three reasons were 1) It’s part of the liberal curriculum that we’re trying to give students of the United States, 2) appreciation for the fact that mathematics is all around us, and 3) it allows us to think in a more organized and efficient way.
I also pointed out in my last post that my karate instructor, an attorney of 35 years, told me that he had never used the quadratic formula in his everyday life. There is another gentleman I know who is a retired attorney. He volunteers at my school, and helps me teach my math classes. Before he was an attorney he was a math teacher who worked in the Cleveland District at East High. He told me that he has used a lot of math in his work, and his background came in handy on several occasions.
Now both of these gentlemen are very intelligent individuals, and they both specialize(d) in matters of law where numbers are important, real estate law and commercial law respectively. Could it be that my karate instructor didn’t use the quadratic formula (or any other type of math like this) because he didn’t know that it could help him? Is it possible that my community volunteer only used math because he knew how to apply it, even though he could have gotten the work done without it? Maybe.
I think another answer to “what’s the point of this?”, which really plays into all three of the above sections, is jobs. Now it’s partially the fault of the schools, curriculum deciders, and teachers (I am guilty) that mathematics becomes the cold and dry subject. But it’s also the fault of the students not to apply what they know to the fields that they enter. But regardless of whether or not people use math in the workplace, the fact is that it can be used in the workplace, and it would be very beneficial to use it in the workplace.
One area of mathematics called discrete mathematics deals with logic and proofs. The world would be a much better place if everyone took discrete mathematics and understood how to apply it. There are the obvious examples like computer programming (a job), which is all logic. But then there less obvious but really important examples like noticing when a politicians make claims that are logically unsound. Sometimes is takes someone trained, but not highly trained, to see the flaw his his/her logic. Then there are geeks like me, who use logic to most efficiently make coffee in the morning (no joke).
If I can use logic, an application of mathematics, to make my coffee in the morning, then I’m sure I would find someway of applying math and logic to my occupation (if it wasn’t being a math teacher). I’m not saying that I would have to use math, nor am I saying that I’d go out of my way to use math. It would just be so ingrained in me, that I’d be using it anyways. This hits on all 3 reasons mentioned above. The logic helps you think in a more organized and efficient manner, it’s part of the curriculum because nobody knows what career path (s)he will choose and how math might play a role, and it’s extremely satisfying knowing that you have come up with a new unique solution to a problem.
This is nice and all, but what about the jobs that will really require the use of higher level mathematics? Let’s see for part 3.

What's the Point of This? (Part 1)

This article is taken from my other website wolf-math.com, while that website is about to be overhauled. Originally posted October 21, 2014.

What's the point of this?

Last night I asked my karate instructor, an attorney for 35 years, if he had ever used the quadratic formula in his professional career. His answer surprised me a bit. He said, “No, but I also took many years of French, and I never had to use that either.”
I know that the quadratic formula applies to more than simple quadratics, because quadratics are found in the most surprising of places (logarithms, differential equations, linear algebra,  etc…). But why are we learning it if students are never going to use it? You can have a great career that pays great money, but never have to use the quadratic formula, or really any math beyond algebra 1. So why learn it, or any type of higher level math if you’re never going to use it?
I think there are three answers to this question. The first answer is that math is part of the school curriculum. That may not seem like a good answer, but I think it’s an excellent answer. Why is it part of the curriculum? A lot of people have this notion that school should be trade school; strictly for obtaining employment.  However, school in the United States (up through college) is not trade school. It is set up to give a liberal education to everyone. That liberal education includes mathematics, science, English/language arts, social studies, and more. Students are learning this for 2 reasons. First of all, nobody knows for certain that they will never use math, so we might as well give them all they can get. Secondly, in a more broad sense, we want the next generation of Americans to be thoughtful and intelligent. We want them to know how to write a letter, how congress works, what The Battle of the Bulge was, how cell division works, and the quadratic formula. Knowledge doesn’t have to be the means towards the end, it can be an end all by itself. There is value in having knowledge, and value in being educated. Education enhances our personal lives by attaining values higher than our basic needs, and it advances our civic lives by being positive contributors to our communities.
We want Americans to be educated because when election time rolls around everyone should know how they’re being affected, or when something is happening in the political scene that you don’t like you can write a letter to your congressman. This answer can apply to most of the school curriculum, but not so much math, or writing haiku, or learning French.
We learn how to write Haiku because we can appreciate its beauty. You can also learn math out of appreciation. Math can be appreciated because of its massive collection of applications, or because of its purity. I’m mostly a pure math person, but I appreciate that all math has application somehow, even if we don’t know yet. What I like about applied math is that I better understand the world around me. I get satisfaction out of knowing that a Google search is a massive exercise in linear algebra, and that throwing a ball has within it the quadratic formula and calculus. Even though I frequently forget how to apply my mathematical knowledge to these applied subjects, I feel good knowing that I have some understanding of how they work. When it comes to pure math I get satisfaction by working hard on a subject and being able to solve the problem. I may not know what I’m try to solve for, but I’ve solved the problem! This leads into the third and final answer, we learn math because it makes us better thinkers.
At my last school I was the only high-school math teacher. I was told by many of my students, colleagues, and superiors that I was so smart and analytic. I sincerely do not believe that I am “smarter” than any of those people who said so. I believe, and I tell my students this, that I am not smarter than any of them, I’ve just been trained in a certain subject matter. Just as the black-belt in karate is good because he practiced his karate, I’m good at math because I’ve practiced math.  Learning this math teaches you to think in a certain way even outside of math class. The black-belt walks out of his dojo not realizing that all of his movements are different, not just his karate moves. Similarly when we walk out of math class we are unknowingly thinking differently about the world. This helps us think “smarter” about things. It hasn’t made us smarter, but we’re thinking in a more efficient way.
There is a fourth reason too, but it is an extension to the first answer. More on that in my next blog post.