Uncategorized – Page 7

Editing Khan

Let’s be clear – I don’t have a problem with most of the content on Khan Academy. Yes, there are mistakes. Yes, there are pedagogical choices that many educators don’t like. I don’t like how it has been sold as the solution to the educational ills of our world, but that isn’t my biggest objection to it.

I sat and watched his series on currency trading not too long ago. Given that his analogies and explanations are correct (which some colleagues have confirmed they are) he does a pretty good job of explaining the concepts in a way that I could understand. I guess that’s the thing that he is known for. I don’t have a problem with this – it’s always good to have good explainers out there.

The biggest issue I have with his videos is that they need an editor.

He repeats himself a lot. He will start explaining something, realize that he needs to back up, and then finishes a sentence that hadn’t really started. He will say something important and then slowly repeat it as he writes each word on the screen.

This is more than just an annoyance. Here’s why:

One of the major advantages to using video is that it can be good instruction distilled into great instruction. You can plan ahead with the examples you want to use. You can figure out how to say exactly what you need to say and nothing more, and either practice until you get it right, or just edit out the bad takes.
I have written and read definitions word by word on the board during direct instruction in my classes. I have watched my students faces as I do it. It’s clearly excruciating. Seeing that has forced me to resist the urge to speak as I write during class, and instead write the entire thing out before reading it. Even that doesn’t feel right as part of a solid presentation because I hate being read to, and so do my students. This doesn’t need to happen in videos.
If the goal of moving direct instruction to videos is to be as efficient as possible and minimize the time students spend sitting and watching rather than interacting with the content, the videos should be as short and efficient as possible. I’m not saying they should be void of personality or emotion. Khan’s conversational style is one of the high points of his material. I’m just saying that the ‘less is more’ principle applies here.

I spent an hour this morning editing one of the videos I watched on currency exchange to show what I mean. The initial length of the video was 12:03, and taking out the parts I mentioned earlier reduced it to 8:15. I think the result respects Khan’s presentation, but makes it a bit tighter and focused on what he is saying. Check it out:

The main reason I haven’t made more videos for my own classes (much to the dismay of my students, who really like them) is my insistence that the videos be efficient and short. I don’t want ten minute videos for my students to watch. I want two minutes of watching, and then two or three minutes of answering questions, discussing with other students, or applying the skills that they learned. My ratio is still about five minutes of editing time for every minute of the final video I make – this is roughly what it took this morning on the Khan Academy video too. This is too long of a process, but it’s a detail on using video that I care too much about to overlook.

What do you think?

Building a need for math – similar polygons & mobile devices

The focus of some of my out-of-classroom obsessions right now is on building the need for mathematical tools. I’m digging into the fact that many people do well on a daily basis without doing what they think is mathematical thinking. That’s not even my claim – it’s a fact. It’s why people also claim the irrelevance of math because what they see as math (school math) almost never enters the scene in one’s day-to-day interactions with the world.

The human brain is pretty darn good at estimating size or shape or eyeballing when it is safe to cross the street – there’s no arithmetic computation there, so one could argue that there’s no math either. The group of people feeling this way includes many adults, and a good number of my own students.

What interests me these days is spending time with them hovering around the boundary of the capabilities of the brain to do this sort of reasoning. What if the gut can’t do a good enough job of answering a question? This is when measurement, arithmetic, and other skills usually deemed mathematical come into play.

We spend a lot of time looking at our electronic devices. I posed this question to my Geometry and Algebra 2 classes on Monday:

The votes were five for A, 5 for B, and 14 for C. There was some pretty solid debate about why they felt one way or another. They made sure to note that the corners of the phone were not portrayed accurately, but aside from that, they immediately saw that additional information was needed.

Some students took the image and made measurements in Geogebra. Some measured an actual 4S. Others used the engineering drawing I posted on the class blog. I had them post a quick explanation of their answers on their personal math blogs as part of the homework. The results revealed their reasoning which was often right on. It also showed some examples of flawed reasoning that I didn’t expect – something I now know I need to address in a future class.

At the end of class today when I had the Geometry class vote again, the results were a bit more consistent:

The students know these devices. Even those that don’t have them know what they look like. It required them to make measurements and some calculations to know which was correct. The need for the mathematics was built in to the activity. It was so simple to get them to make a guess in the beginning based on their intuition, and then figure out what they needed to do, measure, or calculate to confirm their intuition through the idea of similarity. As another chance at understanding this sort of task, I ended today’s class with a similar challenge:

My students spend much of their time staring at a Macbook screen that is dimensioned slightly off from standard television screen. (8:5 vs. 4:3). They do see the Smartboard in the classroom that has this shape, and I know they have seen it before. I am curious to see what happens.

Computational modeling & projectile motion, EPISODE IV

I’ve always wondered how I might assess student understanding of projectile motion separately from the algebra. I’ve tried in the past to do this, but since my presentation always started with algebra, it was really hard to separate the two. In my last three posts about this, I’ve detailed my computational approach this time. A review:

We used Tracker to manually follow a ball tossed in the air. It generated graphs of position vs. time for both x and y components of position. We recognized these models as constant velocity (horizontal) and constant acceleration particle models (vertical).
We matched graphical models to a given projectile motion problem and visually identified solutions. We saw the limitations of this method – a major one being the difficulty finding the final answer accurately from a graph. This included a standards quiz on adapting a Geogebra model to solve a traditional projectile motion problem.
We looked at how to create a table of values using the algebraic models. We identified key points in the motion of the projectile (maximum height, range of the projectile) directly from the tables or graphs of position and velocity versus time. This was followed with the following assessment
We looked at using goal seek in the spreadsheet to find these values more accurately than was possible from reading the tables.

After this, I gave a quiz to assess their abilities – the same set of questions, but asked first using a table…

… and then using a graph:

The following data describes a can of soup thrown from a window of a building.

How long is the can in the air?

What is the maximum height of the can?

How high above the ground is the window?

Is the can thrown horizontally? Explain your answer.

How far from the base of the building does the can hit the ground?

What is the speed of the can just before it hits the ground?</li

I was really happy with the results class wide. They really understood what they were looking at and answered the questions correctly. They have also been pretty good at using goal seek to find these values fairly easily.

I did a lesson that last day on solving the problems algebraically. It felt really strange going through the process – students already knew how to set up a problem solution in the spreadsheet, and there really wasn’t much that we gained from obtaining an algebraic solution by hand, at least in my presentation. Admittedly, I could have swung too far in the opposite direction selling the computational methods and not enough driving the need for algebra.

The real need for algebra, however, comes from exploring general cases and identifying the existence of solutions to a problem. I realized that these really deep questions are not typical of high school physics treatments of projectile motion. This is part of the reason physics gets the reputation of a subject full of ‘plug and chug’ problems and equations that need to be memorized – there aren’t enough problems that demand students match their understanding of how the equations describe real objects that move around to actual objects that are moving around.

I’m not giving a unit assessment this time – the students are demonstrating their proficiency at the standards for this unit by answering the questions in this handout:
Projectile Motion – Assessment Questions

These are problems that are not pulled directly out of the textbook – they all require the students to figure out what information they need for building and adapting their computer models to solve them. Today they got to work going outside, making measurements, and helping each other start the modeling process. This is the sort of problem solving I’ve always wanted students to see as a natural application of learning, but it has never happened so easily as it did today. I will have to see how it turns out, of course, when they submit their responses, but I am really looking forward to getting a chance to do so.

Grouping Problems in 1st Grade

My wife (Josie) was showing me the work she is doing with her first grade students in math. They are talking about grouping tens and ones, ultimately looking to explore place value. Her activity was to have students imagine situations involving collecting groups of items, and then looking at the mathematical structure behind those groups. One wrote about how a thief had a container that could only carry 10 ice cream cones at a time, which meant that he had to leave some of the ice cream cones he was stealing from a house behind. Another talked about the Grinch stealing twenty Christmas trees at a time from a forest that had 255.

There are two things that I really like about the approach. One is that it doesn’t do the common backwards approach I have seen in elementary math programs where the math problem comes first. It seems off to asking students to add 3 + 4 = 7, and then ‘make up a story problem’ that matches this abstract idea. Here, the students are coming up with problems that matter to them, and creating organization (groups) that make sense to them. Going from abstract to concrete works marginally well at best at the high school level for developing understanding, let alone for six and seven year olds that are wrapping their heads around abstract ideas like place value.

I also really like that Josie didn’t push the students to consider only even groupings. (255 trees into groups of 20? There’s a remainder. THERE’S A REMAINDER!) Word problems are often contrived to have even numbers only to make them ‘easier to understand’ and consequently even less real world. I just thought it was neat to see that she is making her students manage that messiness from the beginning.

This is clearly different from the higher level courses that I usually concern myself with in high school, but the idea still transfers well, regardless of the level. It’s always great to see things being done right by the younger students as well.

Simulations, Models, and the 2012 US Election

After the elections last night, I found I was looking back at Nate Silver’s blog at the New York Times, Five Thirty Eight.

Here was his predicted electoral college map:

…and here was what ended up happening (from CNN.com):

I’ve spent some time reading through Nate Silver’s methodology throughout the election season. It’s detailed enough to get a good idea of how far he and his team have gone to construct a good model for simulating the election results. There is plenty of description of how he has used available information to construct the models used to predict election results, and last night was an incredible validation of his model. His popular vote percentage for Romney was predicted to be 48.4%, with the actual at 48.3 %. Considering all of the variables associated with human emotion, the complex factors involved in individuals making their decisions on how to vote, the fact that the Five Thirty Eight model worked so well is a testament to what a really good model can do with large amounts of data.

My fear is that the post-election analysis of such a tool over emphasizes the hand-waving and black box nature of what simulation can do. I see this as a real opportunity for us to pick up real world analyses like these, share them with students, and use it as an opportunity to get them involved in understanding what goes into a good model. How is it constructed? How does it accommodate new information? There is a lot of really smart thinking that went into this, but it isn’t necessarily beyond our students to at a minimum understand aspects of it. At its best, this is a chance to model something that is truly complex and see how good such a model can be.

I see this as another piece of evidence that computational thinking is a necessary skill for students to learn today. Seeing how to create a computational model of something in the real world, or minimally seeing it as an comprehensible process, gives them the power to understand how to ask and answer their own questions about the world. This is really interesting mathematics, and is just about the least contrived real world problem out there. It screams out to us to use it to get our students excited about what is possible with the tools we give them.

First Day Activities: Robotics

For our orientation activities this year, we are focusing on getting to know each other, and discussing/interacting/performing skits around digital citizenship and our school’s computer use policy. To make sure we have enough time for these activities, but find problems with the schedule, we are going through each day of the block schedule with abbreviated classes. This means that each class gets around twenty minutes to meet.

I love the limited time for the sole reason that I’m not even tempted to talk about policies. It’s a chance to do something interesting with the students and whet their appetites for what the class is going to be about. I’m going to share what I did as an opportunity to record what I did on the first day for the future (which I always plan to do, but rarely do) but also to give others ideas.

Robotics

The students came in to find three full Ziploc bags of LEGO pieces – the last of my collection from back home that was previously in storage. I asked them to build a tower as tall as they could build it using the pieces from the bags. I asked that they keep track of the number of bricks they used in their design.

They quickly got to work – I was impressed with how quickly they jumped into team-oriented roles. Some created a base for the tower. Others started stacking bricks. Another occasionally pantomimed a general shape they should try to follow.

After around eight minutes had passed, we measured the tower. I then said they needed to build a tower that reached at least the same height, but used half the number of bricks they used in the first one. Again, they quickly got to work. They scrapped the nice base they had built and did some interesting sideways building vertically to make up for the pieces they knew they had to remove. Eventually the height reached more than twice the height of their original tower – I was impressed.

We then had three minutes left – just enough to ask students to compare this task to building and designing something in the real world. I mentioned the word constraints to describe what they came up with, but they got the idea. They also mentioned that it would have helped if they knew what all of the constraints and requirements were at the beginning. I agreed, with a smirk.

Then it was off to the next class.

It’s good to be back! Expect more posts as I can fit them in.

A Response to Slate: How the recent article on technology misses the point.

Ah, summer. A great time to kick back, relax, and have time to write reactions to things that bug me.

I read through the article on Slate titled ‘Why Johnny Can’t Add Without a Calculator’ and found it to be a rehashing of a whole slew of arguments that drive me nuts about technology in education. It also does a pretty good job of glossing over a number of issues relative to learning math.

The problem isn’t that Johnny can’t add without a calculator. It’s that we sometimes focus too much about turning our brain into one.

This was the sub-heading underneath the title of the article:

Technology is doing to math education what industrial agriculture did to food: making it efficient, monotonous, and low-quality.

The author then describes some ancedotes describing technology use and implementation:

An experienced teacher forced to give up his preferred blackboard in favor of an interactive whiteboard, or IWB.
A teacher unable to demonstrate the merits of an IWB beyond showing a video and completing a demo of an electric circuit.
The author trying one piece of software and finding it would not accept an answer without sufficient accuracy.

I agree with the author’s implication that blindly throwing technology into the classroom is a bad idea. I’ve said many times that technology is only really useful for teaching when it is used in ways that enhance the classroom experience. Simply using technology for its own sake is a waste.

These statements are true about many tools though. The mere presence of one tool or another doesn’t make the difference – it is all about how the tool is used. A skilled teacher can make the most of any textbook – whether recently published or decades old – for the purposes of helping a student learn. Conversely, just having an interactive whiteboard in the classroom does not make students learn more. It is all about the teacher and how he or she uses the tools in the room. The author acknowledges this fact briefly at the end in arguing that the “shortfall in math and science education can be solved not by software or gadgets but by better teachers.” He also makes the point that there is no “technological substitute for a teacher who cares.” I don’t disagree with this point at all.

The most damaging statements in the article surround how the author’s misunderstanding of good mathematical education and learning through technology.

Statement 1: “Educational researchers often present a false dichotomy between fluency and conceptual reasoning. But as in basketball, where shooting foul shots helps you learn how to take a fancier shot, computational fluency is the path to conceptual understanding. There is no way around it.”

This statement gets to the heart of what the author views as learning math. I’ve argued in previous posts on how my own view of the relationship between conceptual understanding and learning algorithms has evolved. I won’t delve too much here on this issue since there are bigger fish to fry, but the idea that math is nothing more than learning procedures that will someday be used and understood does the whole subject a disservice. This is a piece of the criticism of Khan Academy, but I’ll leave the bulk of that argument to the experts.

I will say that I’m really tired of the sports skills analogy for arguing why drilling in math is important. I’m not saying drills aren’t useful, just that they are never the point. You go through drills in basketball not just to be able to do a fancier shot (as he says) but to be able to play and succeed in a game. This analogy also falls short in other subjects, a fact not usually brought up by those using this argument. You spend time learning grammar and analysis in English classes (drills), but eventually students are also asked to write essays (the game). Musicians practice scales and fingering (drills), but also get opportunities to play pieces of music and perform in front of audiences (the game).

The general view of learning procedures as the end goal in math class is probably the most destructive reason why people view math as something acceptable not to be good at. Learning math this way can be low-quality because it is “monotonous [and] efficient”, which is not technology’s fault.

One hundred percent of class time can’t be spent on computational fluency with the expectation that one hundred percent of understanding can come later. The two are intimately entwined, particularly in the best math classrooms with the best teachers.

Statement 2: “Despite the lack of empirical evidence, the National Council of Teachers of Mathematics takes the beneficial effects of technology as dogma.”

If you visit the link the author includes in his article, you will see that what NCTM actually says is this:

“Calculators and other technological tools, such as computer algebra systems, interactive geometry software, applets, spreadsheets, and interactive presentation devices, are vital components of a high-quality mathematics education.”

…and then this:

“The use of technology cannot replace conceptual understanding, computational fluency, or problem-solving skills.”

In short, the National Council for Teachers of Mathematics wants both understanding and computational fluency. It really isn’t one or the other, as the author suggests.

The author’s view of what “technology” entails in the classroom seems to be the mere presence of an interactive whiteboard, new textbooks, calculators in the classroom, and software that teaches mathematical procedures. This is not what the NCTM intends the use of technology to be. Instead the use of technology allows exploration of concepts in ways that cannot be done using just a blackboard and chalk, or pencil and paper. The “and other technological tools next to calculators in the quote has become much more significant over the past five years, as Geometers Sketchpad, Geogebra, Wolfram Alpha, and Desmos have become available.

Teachers must know how to use these tools for the nature of math class to change to one that emphasizes mathematical thinking over rote procedure. If they don’t, then math continues as it has been for many years: a set of procedures that students may understand and use some day in the future. This might be just fine for students that are planning to study math, science, or engineering high school. What about the rest of them? (They are the majority, by the way.)

Statement 3: “…the new Common Core standards for math…fall short. They fetishize “data analysis” without giving students a sufficient grounding to meaningfully analyze data. Though not as wishy-washy as they might have been, they are of a piece with the runaway adaption of technology: The new is given preference over the rigorous.”

If “sufficient grounding” here means students doing calculations done by hand, I completely disagree. Ask a student to add 20 numbers by hand to calculate an average, and you’ll know what I mean. If calculation is the point of a lesson, I’ll have students calculate. The point of data analysis is not computation. Just because the tools take the rigor out of calculation does not diminish the mathematical thinking involved.

Statement 4: “Computer technology, while great for many things, is just not much good for teaching, yet. Paradoxically, using technology can inhibit understanding how it works. If you learn how to multiply 37 by 41 using a calculator, you only understand the black box. You’ll never learn how to build a better calculator that way.”

For my high school students, I am not focused on students understanding how to multiply 37 by 41 by hand. I do expect them to be able to do it. Usually when my students do get it wrong, it is because they feel compelled to do it by hand because they are taught (in my view incorrectly) that doing so is somehow better, even when a calculator sits in front of them. As with Statement 3, I am not usually interested in students focusing on the details of computation when we are learning difference quotients and derivatives. This is where technology comes in.

I tweeted a request to the author to check out Conrad Wolfram’s TED Talk on using computers to teach math, and asked for a response. I still haven’t heard back. I think it would be really revealing for him to listen to Wolfram’s points about computation, the traditional arguments against computation, and the reasons why computers offer students new opportunities to explore concepts in ways they could not with mere pencil and paper. His statement that math is much more than computation has really changed the way I think about teaching my students math in my classroom.

Statement 5: “Technology is bad at dealing with poorly structured concepts. One question leads to another leads to another, and the rigid structure of computer software has no way of dealing with this. Software is especially bad for smart kids, who are held back by its inflexibility.”

Looking at computers used purely as rote instruction tools, I completely agree. That is a fairly narrow view of what learning mathematics can be about.

In reality, technology tools are perfectly suited for exploring poorly structured concepts because they let a student explore the patterns of the big picture. The situation in which “one question leads to another” is exactly what we want students to feel comfortable exploring in our classroom! Finally, software that is designed for this type of exploration is good for the smart students (who might quickly make connections between different graphical, algebraic, and numerical representations of functions, for example) and for the weaker students that might need different approaches to a topic to engage with a concept.

The truly inflexible applications of technology are, sadly, the ones that are also associated with easily measured outcomes. If technology is only used to pass lectures and exercises to students so they can perform well on standardized tests, it will be “efficient, monotonous, and low quality” as the author states at the beginning.

The hope that throwing calculators or computers in the classroom will “fix” problems of engagement and achievement without the right people in the room to use those tools is a false one, as the author suggests. The move to portray mathematics as more than a set of repetitive, monotonous processes, however, is a really good thing. We want schools to produce students that can think independently and analytically, and there are many ways that true mathematical thinking contributes to this sort of development. Technology enables students to do mathematical thinking even when their computation skills are not up to par. It offers a different way for students to explore mathematical ideas when these ideas don’t make sense presented on a static blackboard. In the end, this gets more students into the game.

This should be our goal. We shouldn’t going back to the most basic textbooks and rote teaching methods because it has always worked for the strongest math students. There must have been a form of mathematical Darwinism at work there – the students that went on historically were the ones that could manage the methods. This is why we must be wary of the argument often made that since a pedagogical method “worked for one person” that that method should be continued for all students. We should instead be making the most of resources that are available to reach as many students as possible and give them a rich experience that exposes them to the depth and variety associated with true mathematical thinking.

What my dad taught me about learning.

The first time I saw the word ‘Calculus’, I was staring at the spines of several textbooks that sat on the bookshelf at home. I didn’t think much of them; I knew they were my parents’, and that they were from their college days, but had no other awareness of what the topic actually was. I did assume that the reason there were so many of them was because my parents must have liked them so much. After further investigation, I learned that they were mostly my dad’s books. His secret was out: he must have loved Calculus. I believed this for a while.

When my older brother took Calculus, these books came off the shelf occasionally as a resource, though I don’t know if this was his decision or my dad’s. From what I knew, my brother breezed through Calculus. I know he worked hard, but it also seemed to come fairly naturally to him. I remember conversations that my parents had about not knowing where my brother got this talent from. They admitted at this point that it couldn’t have been from either of them. My dad had taken Calculus multiple times and the collection of textbooks was the evidence that hung around for no particularly good reason.

This astounded my young brain for a couple of reasons. It was mind-boggling to me that my parents ever had trouble doing anything. They always seemed to know just what to do in different situations – how could they not do well in a class designed to teach them something? It was also the first time I ever remember learning that my dad was not successful in everything he tried to do. This conflicted deeply with what I understood his capabilities to be.

As I understood it, he just knew everything.

When I was nine and my parents had bought me a keyboard to learn to play piano for the first time, there was no AC adapter in the box I had unwrapped only moments before. My dad scrounged around among his junk boxes and drawers and found one with the correct tip, but the polarity was wrong. I knew I wasn’t going to be able to start jamming that night – it was late and a trip to the store wasn’t an option. He wasn’t going to submit to that as a possibility – he took the adapter downstairs to the basement and had me follow him. There was soldering involved, and electrical tape. I had no idea what he was doing. Moments later, however, he appeared with the same adapter and a white label that said ‘modified’. We plugged it in to the keyboard and it lit up, ready for me to play and drive my parents crazy with my rendition of . I now understand that he switched the wires around to change the polarity – I did it myself with some students recently in robotics. At the time though, it seemed like magic. I just knew I had the smartest dad in the world.

His mantra has always been that if it can be fixed, it should be fixed, no matter the hilarity of the process. I watched him countless times take in the cast-off computers of other people who asked him if he knew how to fix them. Thinking back, I don’t know that he ever specifically answered that question. His usual response was (and still is) “I’ll take a look.” So he would work long hours with a vacuum, various metal tools, and a gray multimeter (that I think he still has) laid out like a surgeon investigating a patient. I rarely had the patience to sit and watch. I would see the results of his work: sheets of yellow legal pad paper filled with notes and diagrams scrawled along the way. In the end, he would inevitably find a solution, though often at this point the person who had asked him to fix the item had gone and bought a new one. I don’t recall ever believing my dad thought it was a waste.

We also worked on things together to try to get closer in my early teens. We both took tests to get amateur radio licenses. I came to really enjoy learning Morse code and got the preparation books to climb the license ladder. He commented repeatedly as I zipped through the books about memorizing the books and not understanding the underlying theory of resonant circuits and antenna diagrams. That was true – at the time I just wanted to pass the tests. I didn’t understand that the process of learning was the valuable part, not the end point. I didn’t see that. I just continued to believe that the tests were a means to an end, just as I viewed through my thirteen year old brain that his herculean efforts to fix things was a means to getting things fixed., and nothing more.

My dad is one of the smartest people I know. As I’ve grown older, however, I have come to understand that it wasn’t that about knowing everything. He instead had been continuously demonstrating what real learning is supposed to be. It was never about knowing the answer; it was about finding it. It wasn’t about fixing a computer, it was about enjoying figuring out how it can be fixed, however much frustration was involved. It wasn’t just about saving money or avoiding a trip to the store to buy an electric adapter. It was about seeing that we can understand the tools we use on a regular basis well enough to make them work for us.

I have seen time and time again how he mentors people to make them better at what they do. I have seen it in the way he mentors FIRST robotics teams as a robot inspector at the Great Lakes regional competition in Cleveland. I have seen it in the way he has spent his time since selling the company he founded with partners years ago. He chooses to do work that matters and makes sure that others are right there to learn beside him. There were times growing up when, admittedly, I just wanted him to fix things that needed to be fixed. To his credit, he insisted on involving me in the process, even when I protested or became impatient.. I didn’t see it when I was younger. Knowing how to go about solving problems is among the most important skills that everyone needs. I was getting free lessons from someone that not only was really good at it, but cared enough about me to want me to learn the joy of figuring things out.

One of my students this year was really into electronic circuits and microcontrollers. He soldered 120 LEDs into a display and wanted to use an Arduino to program it to scroll text across it. The student’s program wasn’t working and he didn’t know why. I had only been tangentially paying attention to the issues he was having, and when he was visibly frustrated, I pulled up a chair and sat next to him, and then said ‘let’s take a look.” We went through lines of code and found some missing semicolons and incorrectly indexed arrays, and I asked him to tell me what each line did. I was only a couple steps ahead of him in identifying the problem, but we laughed and tried making changes while speaking out loud what we thought the results would be. At one point, he said to me “Mr. Weinberg, you’re so smart. You just know what to do to fix the program.”

I immediately corrected him. I didn’t know what was wrong. We were able to make progress by talking to each other and experimenting. It wasn’t about knowing just what to do. It was about figuring out what to try next and having strategies to analyze what was and was not working. I learned this from a master.

On this Father’s day (that also happens to be the day before my dad’s birthday), I celebrate this truth: much of what I do as a teacher comes from trying to channel my dad’s habits while confronting big challenges. I don’t want my students to memorize steps to pass tests; I want them to understand well enough to be able to solve any challenge set before them. I don’t want to fix my students’ problems – I want to help them learn to fix problems themselves. I don’t want my students to be afraid to fail; I want them to understand through example that failure leads to finding a better way.

I am grateful for all that I have learned from him., and I try to teach my students what he has taught me about learning at every opportunity. It would be fine by me if I ever need to do Calculus for him – I’d still be in the red.

End of year reflections – SBAR analysis

I wrapped up grading final exams today. Feels great, but it was also difficult seeing students coming in to get their final checklists signed before they either graduate or move on to a different school. Lots of bittersweet moments in the classroom today.

I decided after trying my standards based grading (SBG) experiment that I wanted to compare different students’ overall performances among the grading categories to their quiz percentages. In a previous post, I wrote about my experimentation doing my quiz assessments on very specific skill standards that the students were given. As I plan to change my grading to be more SBG based for the fall, I figured it would be good to have some comparison data to be able to argue the many reasons why this is a good idea.

In my geometry and algebra two classes, there are 28 total students. I removed two students from the data set that came in the last month of school, and one outlier in terms of overall performance.

The table below shows the names of each grading category, as well as the overall grade weight for the category used in calculating the grade. The numbers are the correlation coefficient in the data between the variable listed in the row and column. For example, the 0.47 is the correlation between the HW data and the Quizzes/Standards data for each student.

	Homework (8%)	Quizzes/Standards (12%)	Test Average (48%)	Semester Exam (20%)	Final Grade (100%)
HW	1	0.47	0.41	0.36	0.48
Quiz/Stndrds		1	0.89	0.91	0.95
Tests			1	0.88	0.97
Sem. Exam				1	0.95
Final Grade					1

Some notes before we dive in:

The percentages do not add up to 100% because I am leaving out the portfolio grade (8%) and classwork grades (4%) which are not performance based.
Homework is graded on turning it in and showing work for answers. I collect and look at homework as a regular way to assess how well they are learning the material.
The empty cells are to save ink; they are just the mirror image of the results in the upper half of the matrix since correlation is not order dependent.
I know I only have 25 samples – certainly not ready for a research publication.

So what does this mean? I don’t know that this is very surprising.

Students doing HW is not what makes learning happen. I’ve always said that and this continues to support that hypothesis. It can help, it is evidence that students are doing something with the material between classes, but simply completing it is not enough. I’m fine with this. I get enough information from looking at the homework to create activities that flesh out misunderstanding the next time we meet. The unique thing about homework is that it is often the first time students look at the material on their own rather than with their peers in class.
My tests include some direct assessments of skills, but also include a lot of new applications of concepts and questions requiring students to explain or show things to be true. It’s very gratifying to see such a strong connection between the quiz scores and the test scores.
I always wonder about the students that say “I get it in class, but then on the tests I freeze up.” If there’s any major lesson that SBG has confirmed for me, it’s that student self-awareness of proficiency is generally not great without some form of external feedback. If this were the case, there would be more data with high quiz scores and low exam scores. That isn’t the case here. My students need real and correct feedback on how they are doing, and the skills quizzes are a formalized way to do this.
I find it really interesting how close the quiz average and the semester exam percentages are. The semester exam was cumulative and covered a lot of ground, but it didn’t necessarily hit every single skill that was tested on quizzes. There were also not quizzes for every single skill, though I tried to hit a number of key ones.

This leads me to believe that it is possible to have several key standards to focus on for SBG purposes, and also to dedicate time to work on other concepts during class time through project based learning, explorations, or independent work. It’s feasible to assess these other concepts as mathematical process standards that are assessed throughout the semester. It strikes a good balance between developing skills according to curriculum but not making classes a repetitive process of students absorbing procedures for different types of problems. I want to have both. My flipping experiments have worked well to approaching that ideal, but I’m not quite there yet.

I’ll have more to say about the details of what I will change as I think about it during the summer. I think a combination of using BlueHarvest for feedback, extending SBG to my Calculus and Physics classes, and less emphasis on grading and collecting homework will be part of it. Stay tuned.

What my mom taught me about patience.

Looking back over the students I’ve taught over the past nine years, I can say that I’ve worked with some phenomenal youngsters. Many of the proudest moments have been those that have required a great deal of patience in moving them forward and helping them develop. There are many times when I’ve felt I owe it to the world to be patient because, well, I know others were patient with me. When a toddler sits behind me and plays the ‘kick-the-seat’ game on a flight, I just sit and take it. I played that game. Actually, I did worse – I perfected an imitation of the call-button ping so that flight attendants would hear the sound, and then look around frantically for the light indicating which row needed attention. I would giggle hysterically; my mom (I assume) hid her face and shook her head.

ejmd — Me, Josie, and my parents in a Shanghai garden, during my parents’ visit to China last fall.

My mom’s patience has always been boundless. When I would make messes in the kitchen with my experiments, she would kindly ask that I clean up after myself. In the many cases that I didn’t, she would remind me, often while I stirred my chocolate milk, loudly. Then I would slurp it, spoon by spoon, each successive clink of the spoon on the glass louder until she would snap, screaming my name sharply to tell me to just drink it. One more clink, then compliance.

I wasn’t the only one that pushed the limits of her sanity. As the middle child of three brothers, we were the worst/best when we worked toward the common goal of mayhem in her midst. Shopping trips at the grocery store were opportunities to get extra things into the cart. In spite of her vigilance, we often succeeded in getting giant rubberband balls, quart containers of honey, and boxes of sugar cereals she subsequently kept from us.

In spite of all of the ways we tested her, she still went out of her way to give us the enriching experiences that shaped who my brothers and I have become. She signed me up for magic lessons at the library. She not only tolerated my interests in collecting insects and animals and getting unbelievably muddy during the process, but scrounged up things like mason jars and film canisters and all the books, field trips, and camps she could find to learn to do these things well. She has always kept me honest. She would look up the facts I claimed were true to see if I was full of it, as I had repeatedly proven I could be. She was the one that broke the news to me that the reason my hamster couldn’t walk that morning because it had a tumor. After tolerating my tears and anger in the midst of the devastating tragedy this was for me at the time, she followed with a completely straight-faced phone conversation with a veterinarian about how one might go about putting down a hamster.

One of the reasons I can maintain a positive outlook on things is that I know that good people are looking out for me. I do my best when people demand the best I have to offer, but understand that there will always be setbacks and failures along the way. My mom was doing this long before I ever realized or appreciated it. Striking the balance between being strict and direct with rules and directions and granting the freedom to try and explore and learn from one’s mistakes is the hardest part of being a teacher. But I get to go home and try again the next day with my students. She put up with my stomping around and singing for no pay in the same house, and had only a crossword puzzle to hide behind.

She managed this balance like a pro, despite the working conditions. I still push her buttons and put my smelly feet on the kitchen table. She shoots the same look she gave me when I was nine. This sort of consistency is rare. It is also what makes me smile knowingly when my students start playing the button-pushing game with me. I just smile and nod to defuse the situation, and that works well enough for me.

The thing I can never get right in the moment, however, the secret that I think my mom had figured out from the beginning is this: she always let me think I had won. I could go on to torture one of my brothers; she could get back to taking care of the important stuff, and being entertained by seeing us battling with each other. I can’t say for sure that this was her tactic. She knew a lot more than she let on when I was younger, but has always been modest enough to just say that I knew how to drive her crazy. I think that is true. I have this sneaking suspicion though that she has always had the upper hand.

I wish her a wonderful Mother’s day. I am committed to trying to be as patient with my students as she was with me, as well as to leaving my dirty socks on her computer in the near future. For the record though: I maintain that Ben was involved in the sandwich incident that resulted in my head getting cracked open.

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