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.
Thursday, July 28, 2011
Tuesday, July 26, 2011
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:
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.
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.
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.
Sunday, July 24, 2011
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.
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.
Thursday, July 21, 2011
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!
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!
Subscribe to:
Posts (Atom)