Summer School - Day Thirty - Report Cards

Last day of summer school. Students pick up report cards.

I am thinking about the inadequacy of our reporting system. Specifically 3 things are bothering me:

1. Percentage Grades
Most of my students have a high C+ or low B. What does that mean? No really! Do they understand 74% of the material? What material? What do they know and what do they still have trouble with? How is 74% different from 72%? One is a B and the other is not... why? Is the 74% student who coasted and did little studying really a better student than the 72% who worked really hard?

2. Demonstration of Learning (Growth)
My students have essentially one or two chances to demonstrate learning of any given topic. That's it. Even if they learn it later and demonstrate their new understanding on a final exam, that old failed quiz still haunts them. How much better if they demonstrate mastery in the future, this new data replaces the old? After all, their new knowledge has replaced their misunderstanding. Why can't new grades replace old ones?

3. Specificity of Learning
What do they not understand? What specific topics gave them trouble? Was it conceptual or procedural? If they didn't get the Pythagoras question, was it because they don't understand the theorem? Or because they have poor algebra skills? Or because they mixed up the legs and hypotenuse? I want to know! And really, the student needs to know in order to improve.

Enter standards-based grading. The more I read, the more I like. The B.C. curriculum is organized with specific learning outcomes and achievement indicators. It is a fairly simple task to map these indicators to standards and start tracking student progress in a more specific manner.

The great thing about it is not how it tracks growth or how it gives more specific information. Although that is great. The great thing is how this system helps students learn. It gives specific feedback, time for remediation, and opportunities to demonstrate growth.

The irony of this is how students react. They are addicted to grades. Even as I type this there is a student in my class complaining of how she failed French because she got an 82%.  She will need to go through grade withdrawal. I explained the new system and its benefits and she is terrified. But I know the new system will help her learn.

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 Twenty-Eight - Review

My summer school class is reviewing for the Provincial Exam, a standardized test required for all grade 10 math students. Fortunately, I have sample exams to help prepare students for what they are likely to see on the exam. In the summer, it is an e-exam. For many students, this will be their first look at an e-exam. Today we tried a sample e-exam from the Ministry of Education website.

The problem with review like this for a class like this is that most students just write the exam as if it were the real exam. When they get to a question they are unsure of, they guess. There is no real attempt to understand the problem and really no value in the review. At the end of the e-exam there is a summary sheet that shows which questions were answered correctly and incorrectly and gives the correct solution. Few students used this data to go back and review concepts unless I specifically asked them to. And then they just went back and guessed again.

What really works for review? Physics! Blog! has some great ideas here and here. But these are for Honours Physics. I am dealing with unmotivated remedial math students in summer school. I wonder what a truly effective review activity would look like in this class.

Summer School - Day Twenty-Seven - Assessment

As summer school winds down, students are scrambling to complete projects and missed quizzes in a desperate attempt to boost their grade. They cram for a few minutes and then ask for a quiz. I give them a simple problem and watch them scratch out some incoherent scribbles. Even if they get the answer, it is clear that there is no understanding and no retained learning.

Over the summer, I have been reading a lot about standards-based grading. I think a system like this would correct a lot of the problems cited above. Students would not be scrambling because every standard is reassessable (is that a word?) at any time. They would not be cramming because standards are assessed throughout the course and reflect sustained learning and growth. There would be no incoherent scribbles because students would have a clear understanding of the standard to be assessed.

The biggest problem I have right now is that if a student does not complete a project, I have no data on that particular concept (standard) and the student receives a zero. This may not be because they do not understand or cannot demonstrate mastery. Perhaps the are just lazy or content with their current grade. Either way, it is not a good reflection of their actual learning of concepts in the course. The last minute cramming is more for my benefit than for theirs.

So many things about how I teach are beginning to irk me. This is good. It makes me question what I do and why I do it. I may not get to full blown standards-based grading this school year. But it is on my mind.

Summer School - Day Twenty-Six - Projects

My summer school students are working on a couple of trigonometry projects. One is a completely contrived problem involving an intricate roof line. Students must calculate various lengths and angles. The other requires that they estimate and calculate lengths and angles in the classroom using a metre stick and clinometer.

I question the value of these projects. They are decent enough as review of the basic concepts. And it does set the topic in a real world context (sort of). But I don't think it really challenges the students to see how math is used in the real world.

This course is specifically designed for students who are going to enter the trades. It seems like a better use of our time would be to go to a construction site where they are building a roof and see how the carpenters solve the problems of lengths and angles. I'm not sure they are using a whole lot of trigonometry on the work site.

I wonder what a real meaningful project would look like.

Summer School - Day Twenty-Five - Learning By Playing

The new curriculum in British Columbia suggests that mathematical skills are best learned in a problem-solving context. First, concretely through the use of manipulatives, then pictorially to represent concepts, and finally symbolically, making the full leap to abstract representations.

I'm still trying to wrap my head around what this would look like in a classroom. I had thought to use summer school as an opportunity to try out some new strategies and methods. But that hasn't happened as much as I would like. Although I have spent most of the summer pondering the implications of this approach.

It seems to me that this is exactly how children learn best. Children play with stuff. My one year-old puts everything in her mouth. She shakes it. She drops it from her high chair... over and over again. She passes it to me... then takes it back, She rolls it on the floor. She tries everything she can think of. Then discards it for something else.

My three year-old is the same. Just less drool. She pokes and prods and swings and shakes and rolls and throws and hides. She tries stuff. She loves soap as a play thing. She paints it, keeps it in her purse and uses it as money. Old store fliers are perfect for her projects. She demonstrates unique and creative ways to use common household items.

I think teenagers are the same. Watch them skateboard... or play video games. They explore and experiment. They try to break things until they figure out its limits and how it works. They are engaged and they persevere through failure.

I think our classrooms ought to give them the same opportunities.

Summer School - Day Twenty-Four - Lunch With Colleagues

One of my favourite pastimes is lunch. Eating out at a restaurant with friends. A nice break from the daily routine. Good food, good conversation, lots of laughter.

As a teacher, I don't often get the opportunity to go to lunch with colleagues. It is one of the privileges that most people in the business world take for granted. So, today, when I had a chance to sit down with 2 of my colleagues over burgers and sandwiches, I jumped at it.

The ability to talk with colleagues about our struggles, problem students, learning styles, lesson plans is one of the most important aspects of reflective teaching. Sometimes just venting can reinvigorate us for the stretch ahead.

But, at its best, collegial conversation is more than letting off steam. It allows us to connect with like-minded professionals who share our pain and our joy. It allows us to refine our ideas and strategies. It allows us to see teaching from a new perspective and challenges our most deeply held assumptions.

It allows us to rediscover our passion.

Thanks Kelly and Blair.

Summer School - Day Twenty-Three - Advanced Students

In Summer School, I am finding it difficult to adequately address the needs of my one advanced student. I know he is only taking this course for "fun" and intends to take more challenging math in the regular school year. He is quietly biding his time. But, I would like to challenge him more.

I have given him several puzzles related to the topics we are covering. The results are challenging my understanding of advanced student. He is quick with the basic material and leaves the rest of the class behind. He clearly grasps concepts quickly and can explain his thinking well. But the puzzles have exposed a weakness in lateral thinking and creative problem solving.

For a long time I have questioned how teachers talk about smart students. I think we label too quickly. When a student repeats back to us what we taught and does so with a minimum of help from us, we think they are bright. And they are. But they really have demonstrated little real learning beyond the ability to memorize.

I want to challenge students to think for themselves. I want to see students think deeply about concepts and be able to articulate their understanding. I want to see students make intuitive leaps without my guidance. I want to see students try creative ways to solve problems and succeed... or fail. I want to see students respond to failure with excitement and more drive to succeed.

I want to see advanced students show advanced thinking.

Summer School - Day Twenty-Two - Guest Post

I am away on holidays. Today's guest blogger is...

Summer School - Day Twenty-One - Great Schools

It is B.C. Day and my family and I are up north at Jack Frost Lake.

I am watching my 3 year old daughter interact with other kids and wondering what her schooling will be like. She just started pre-school this year so my wife and I are starting to think about her future in the public education system. We have lots of choices.

What school do we want her to go to? Do we want her to be in French Immersion? Do we move to an area with a better school? What defines a better school? How do you know? The Fraser Institute would say standardized test scores and graduation rates are prime indicators of a strong school. But there must be more to it than that.

I want my daughter to have a rich learning environment that includes the arts, sports, music, social justice and clubs. I want my daughter to be challenged to think, to explore her creativity, to try... and fail... and try again. I want her to have teachers like the ones I work with every day who see student learning as the ultimate goal and research, create and innovate to make it happen.

Educational issues become so much more important when it's your kid you're talking about.

Summer School - Day Twenty - Guest Post

I am away on holidays. Today's guest blogger is...

Summer School - Day Nineteen - The Calculus of Learning

Differentiation is a buzz word in my district. Finding ways to adapt lessons to address a variety of learning styles and learning paces. Creating problems and activities that allow all students to engage and work at a level that is appropriate to them. Differentiation... students working at different rates, different slopes.

It is a fairly simple task to remove complexity from a problem. It is another thing altogether to create a simple learning activity that still challenges students to think, wrestle and learn. An activity with more than one entry point that will allow struggling students to tackle the same basic concepts while advanced students apply those concepts in challenging contexts. Different learning slopes.

How this will apply in my physics classes next year? Most students who take physics would be classified as advanced. But, as I transition to a modeling-based method of teaching, I wonder how the variety of learning styles will respond. I wonder how many different learning slopes will be needed to ensure all students are successful.

Summer School - Day Eighteen - Cheating

I am giving daily homework quizzes as a way to assess student progress in the rapidly paced world of summer school. Cheating is rampant. It's a small room with no dividers. Temptation is strong.

But, there is a larger underlying reason why students cheat. They are embarrassed by their lack of understanding. And that is my fault, not theirs.

Students who are truly interested in learning, who are engaged in the subject matter, who want to demonstrate their own learning will have no desire to cheat.

Summer School - Day Seventeen - Even More Helplessness

At the beginning of a new unit about angles, I focused on vocabulary. There is a glossary in the back of the textbook that students used to look up words like acute, obtuse, transversal, complimentary, etc.

I never thought they would have trouble with the definition of the word "angle".

Apparently the textbook writer's didn't think so either because a definition for angle is nowhere to be found. So, I began to probe and ask for students to tell me what an angle is. I knew I would not get a rigorous mathematical definition, but I expected some understanding of the concept. A girl suggested, "In a shape, it's the corner." A decent beginning. I hoped for others to build upon that idea.

Nothing.

Complete silence.

I realized some of them had ideas but weren't going to share. Others had no clue. Still others could care less. They expected me to give up and tell them the answer. I refused. I told them:

"I know what you're doing. You think I'm going to break down and tell you the definition. Well, I'm prepared to wait you out."

I made each table discuss and come up with some definition. Wrong answers were OK, even good as a starting point for learning. But, every table had to have some reasonable definition. Then I would randomly call on one member of the group to share.

This worked pretty well. We had some interesting ideas and I tried to use Socratic questioning to get at student's underlying thinking and assumptions. I had limited success. Eventually I dragged them kicking and screaming to the idea that an angle was a measure of rotation in the same way length was a measure of distance.

The point of all this is not the students lack of understanding of what an angle is. It is my lack of ability to draw out what I am sure they already intuitively know... an angle measures rotation. I need so much more practice at Socratic questioning. I need to plan ahead and script a discussion so I can anticipate likely misconceptions and difficult concepts.

I was excited about the overall effectiveness of the discussion despite it's unimpressive final results. As I tell my students, initial failure is good if it moves us towards understanding and learning.

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 Fourteen - More Helplessness

We are doing a garden design project as a follow up to our measurement unit. Using grid paper where 1 square equals 1 foot, a student needs to draw and cut out a square planter with side length 2' 4". He comes  to me to ask how to do this. Fair enough. 4" can be tricky. It is a fraction of a foot.

The conversation below occurs more or less as follows (at several different times, with the same student and with other students):

Me:   How much of a foot is 4 inches?

Student:   2.4

Me:   No, just the 4 inches.

Student:   Oh, 0.4.

Me (thinking):   He's stuck in a base 10 metric system. Let's try something else.

Me:   OK. How many inches are in half a foot?

Student:   50.

Me (thinking):   What?!?! Oh! He means 50%.

Me:   How many inches are in half a foot?

Student:   50.

Me:   No. Inches. How many inches?

Student:   Oh, 0.5.

Me:   You are thinking about 50% right? I am asking you how many inches?

Student:   50?

Me:   OK. How many inches in a whole foot?

Student:   What? Ummmm 12.

Me:   Right! So how many inches in half a foot?

At this point, the student starts writing ratios to do a unit conversion, converting 4 inches to feet. Then he grabs his papers and says, "I'll work on it." But, he doesn't really work on it. Later when I drop by to see his progress, he has nothing. But he stills wants me to draw 2' 4" for him.

It is so much easier to just draw it for him and walk away. Miraculously, I resist this urge and proceed to have another conversation as before. This time, he gets it (at least he guessed the right answer) and he draws the square.

But now, there is a circle with radius 1' 3". Oh No!

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 Twelve - Little Something New

In my last post, I described my frustrations with how my teaching is reverting to basic lecturing with worksheets this summer. I am so sick of talking. I see the glazed expressions and I know there is no transfer of knowledge happening. Then I have to talk more later because (a few) students have questions if the assignment differs from the notes even by a little.

So, today I tried something new. Nothing spectacular... just an attempt to get them thinking on their own. To introduce surface area, I posed a simple problem:

   I have a rectangular box I need to wrap for a birthday present.
   Given certain dimensions, how much wrapping paper do I need?

In small groups students worked together to determine an answer, but also explain what they were doing and why. Throwing numbers on a page and calculating does not demonstrate any understanding of the concept of surface area.

Group 1 - Absolute silence. I come back in 5 minutes and they still aren't talking. Although, one of them has written a potential answer on paper without consulting her teammates. Wrong answer.

Group 2 - This group includes the boy recently arrived from India who has already taken calculus. Correct answer but he is the only one who understands it.

Group 3 - A decent discussion emerges. Half the group has calculated volume. They saw a bunch of numbers on the diagram and started doing some math. Their explanation amounts to, "Isn't this what your supposed to do?" One girl in the group is suggesting the correct method. When I ask her to explain her thinking, she has some vague recollection of doing this before. So in effect she is fishing for a mathematical technique that some other teacher taught her last year. No conceptual understanding. Just matching the right method with the right problem.

Group 4 - Also volume calculation. Although one student has the correct answer on his own. He understands that the front face is the same as the back, etc. But still no real understanding of surface area as a concept.

Group 5 - One student has drawn a diagram of each face and calculated the perimeter for each. Then he erased it all when he saw me coming. I try to tell him, I like his method and he is on the right track but he interrupts me to say he was just messing around.

Conclusions? The activity was not stellar but then it was not meant to be. All I wanted to do was get them thinking. Unfortunately the extent of their thinking was to try to remember what another teacher taught them once long ago. Some randomly multiplied numbers. Others started on an interesting path only to fall victim to self-doubt.

These students in particular are not used to thinking for themselves. It will take a lot more than one simple problem to break the culture of learned helplessness. I am going to try to introduce each remaining topic in a similar way. And after each chapter test, we will work on a project that should get them thinking.

Baby steps.

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.