Summer School - Day Twenty-Nine - Teacher Thoughts

An informal poll of 3 other physics teachers at summer school reveals the following:

1. Most physics teachers use the majority of class time to lecture yet acknowledge the limitations of lectures.
2. Most physics teachers do some demonstrations or activities to teach concepts.
3. Most physics teachers would like to do more labs but have little or no equipment.
4. Most physics students love labs and activities.
5. Most physics students don't like writing lab reports.
6. Most physics teachers don't like marking lab reports.
7. Most physics teachers grade based on quizzes and tests.
8. Most physics teachers do NOT use standards-based grading.
9. Most physics teachers are a little afraid of standards-based grading.
10. Most physics students are wary of standards-based grading.

Summer School - Day Sixteen - Teaching to the Exam

Quick thought.

While teaching similar triangles, I found myself working three specific examples for my students because I know these are the types of questions they will see on the exam. Instead of focusing on concepts like corresponding parts, scale factor, and ratio, I taught procedures for solving each of the "tricky" types of problems. I pointed out why the questions were "tricky", what to keep in mind and how to set up the "correct" mathematical procedure.

Knowing what is going to be on the exam often leads me to poor teaching. I want to make sure I cover all the possibilities and prepare my students for the problems they will see. Of course, deep conceptual understanding coupled with the confidence to think through a new problem would work just as well. Probably better.

I guess I'll see the result of my efforts tomorrow on the test.

Update:  Despite (or maybe because of) my explanations yesterday, at least 3/4 of the class still answered the "tricky" questions wrong. They made all the same mistakes I warned them about demonstrating both poor procedural knowledge and a complete lack of conceptual understanding. This just deepens my convictions about 2 things. One, teaching procedures without concepts is next to useless. Two, words are a poor way to communicate concepts.

Summer School - Day Fifteen - Half Way

Half way reflection.

Accepting a summer school position was supposed to be a little extra money, a way to keep busy in the morning, and most importantly a chance to try some new things. A whole summer off seemed like it would ensure that I continue to teach the same way come September. Teaching a summer class gave me the opportunity to keep thinking about change and try out some new ideas before implementing them in my classroom in the fall.

Hasn't happened.

Besides the obvious lazy summer excuse, there are several other factors that have limited my good intentions. Family demands, trip planning, pregnant sister-in-law, sick kids, challenges at church... all these things dominate my thinking during the course of a day. And when my thoughts do turn to teaching strategies, I am focused on the new year not on the summer course.

The good thing is that by lecturing and giving worksheets during the summer, I have found lots of time to read blogs and articles, review grading standards, and follow twitter. All of these things are continuing to shape my thinking and help me plan for the new school year. If it wasn't for summer school, I would not have the time to dig deep like this. I would be too busy recovering from a day of Vacation Bible School and swimming lessons followed by a weekend of gymnastics.

Teaching summer school has given me time. Time to research. Time to reflect. Time to write.

Time to think.

Summer School - Day Thirteen - Learned Helplessness

My colleague-across-the-hall, Blair Miller, and I talk a lot about the culture of learned helplessness in our school. Basically, it comes from teachers being too helpful. So when we actually ask students to think for themselves or work through a problem, they have no motivation, no skills, no idea what to do. The default response is to ask for help and expect the teacher to do most of the work for them. And why not? That's the way it has been for years.

The danger of this crystallized for me today when my summer school class wrote a chapter test.

UPDATE: Day after test. It's happening again right now. For a garden design project, a student is asking me how to fit a 25x40 foot rectangle onto a grid that is 26x42 squares. It takes us 5 minutes to figure out. And he still wants confirmation as he crosses out the extra rows. AARGH!

The most common question during the test was, "How do I do this again?" And there was a sense of expectation that I would just give them the answer. And frustration and bafflement when I walked away instead.

UPDATE: I just went to check on the student's progress. He had crossed out 3 rows instead of 2 to get a 25x39 rectangle. Then he accused me of not explaining it right. His friend says, "We're A&W math (remedial). What do you expect?" I expect you to be able to subtract! Double AARGH!

I know the fault lies with me not with the students. If they engage in this learned helplessness, it is because I allow it, even encourage it by my need to explain everything. I wonder if it's a control issue? I want to be in charge of what is learned and how it is learned. My way is the best. But, clearly it is not.

I see the modeling method of teaching as more than just a superior way to teach math and physics. It teaches independent learning. It forces students to wrestle with concepts and explain their thinking. It exposes misconceptions. It creates opportunities for students to build deep and rich understanding.

It allows me to be less helpful.

UPDATE: Full disclosure. Turns out I was wrong. Triple AARGH! The gird is 27x41 not 26x42. But the student still had it wrong and did not understand the concept of subtraction in this context. Why am I justifying myself? I really do need to get out of the way.

Summer School - Day Eleven - Bad Teaching

It's official... I have already given up trying to plan new things for summer school. I have reverted to stand and deliver and here's the worksheets. Of course this means that 5 minutes after my spectacular explanations with examples, I have a line of kids asking questions. "How do I do this?"

Who am I kidding? It's not a line of kids. It's about 3. The rest of them still don't know what to do but they don't bother asking. And this lack of caring from the students contributes to my own ennui. Teachers talk a lot about engaging students, getting them excited and interested and motivated. What about the students' responsibility to reciprocate?

My colleague-across-the-hall, Blair Miller, and I talk a lot about the culture of learned helplessness at our school. A big part of the problem is exactly the kind of teaching I am currently doing in summer school. It creates a climate in the classroom where students expect the teacher to spoon feed them everything they need. And we accommodate them.

Teacher lectures. Teacher gives notes. Teacher gives assignment... but wait! Here is a problem that is not exactly like the notes. I'm lost! Teacher walks through the problem so I don't have to think. I now have correct answers on my page and absolutely no understanding. But that's OK because teacher will spoon feed me again tomorrow.

I plan to make one minor change tomorrow. I am going to introduce the concept of surface area by getting students in groups to figure out how to wrap a present. No spoon feeding. They must work it out together.

I admit, I am not optimistic.

Summer School - Day Seven - Questions, Questions

I have 5 students out of a class of about 20 that actually ask me questions in class. Most of these questions are of the "Am I doing this right?" variety. No one else bothers. And this is not a class of stellar mathematicians.

One of the 5 is that persistent, pestering type that wants help on every detail and every step. He really doesn't want to know the reasons why. He just wants me to tell him the proper steps. If I try to explain the reasoning instead, he interrupts me with statements like "So, then I do this or that?" Inevitably he is wrong, because he isn't listening to the amazing math reasoning pouring forth from my mouth.

I've been thinking about being less helpful to my students. The problem is, in this case, with so little time in summer school and students who are not really motivated to learn but just want to get through and pass, being less helpful basically severs the lifeline they are clinging to. They are drowning in a sea of indecipherable math and are grasping at any floating object that might drift by.

I am getting really tired of standing in front of a class and talking. I get so frustrated trying to explain deep concepts when all they want is procedures that get the right answer. But if I stop throwing floating objects, they drown.

Summer School - Day Three - Stifling Student Creativity

Quiz question today:

     The wholesale price of a hat is $9.00. It is marked up by 75%.
     What is the final retail price?

Since this is Apprenticeship & Workplace Math, most of my students have struggled with math for years. They likely have failed this very course at least once before. So, I am attempting to simplify things as much as possible. I am teaching them one mathematical tool that they can use for almost every problem they will encounter in the course... ratios and proportions.

It works something like this (for the above problem):

      75     =    x  
     100      $9.00

     Then cross-multiply and divide to get the markup amount
     Add the markup to the wholesale price and voila! you get the retail price

I know what you're thinking. The quiz question is less than stellar to begin with. And teaching procedure-based mathematics completely misses any real conceptual understanding. But, remember, my main goal here is to give my struggling students one procedure that they can learn well and use for almost every problem they see.

You would think this would be appealing to my students. But the resistance is incredible. They want to use various other techniques they half-learned last year and sort of remember. Most of the time the results are disastrous. But occasionally there is a flash of brilliance.

Hank answered the above question correctly. At least the final answer was correct. But the steps he used to get there were baffling to me. Numbers appeared as if by magic. But somehow the final answer appeared at the end. It took me a while to figure out what he was doing. So, I decided to ask him to explain himself to see if he understood what he was doing. And he did.

His reasoning went like this:

• I know 10% of $9.00 is 0.90. I just moved the decimal point to the left.
• Then I multiplied 0.90 by 7 because 7 x 10% is 70%. I got 6.30.
• Then I divided 0.90 by 2 because 10% divided by 2 is 5%. I got 0.45.
• Then I added 6.30 + 0.45 because 70% + 5% is 75%. I got $6.75.
• Then I added $6.75 + $9.00 to get the retail price. It is $15.75.

Wow! I think this demonstrates a pretty good grasp of numbers, percents and multiplication. Not to mention a fairly unique problem solving strategy. I never would have thought of this. Maybe I shouldn't be surprised when students do stuff like this. But I still am.

I do believe there are some potential problems with this method:

• This approach is much less efficient than my proportion method
• It is much more difficult when the markup is 63.7%
• With so many calculation steps, this method opens the door to simple arithmetic mistakes
• One simple strategy that works for all problems is easier than trying to remember several unique strategies that only work for specific problems

So, how did I respond? I told Hank what great thinking this was. I congratulated him for demonstrating strong problem solving skills. I explained the potential problems with his approach. Then I told him to do it my way.

And I admit... a little piece of me died when I said it.