0 Today's Million Dollar Question

I have been struggling a bit this year with getting a student or two to show steps/process/work/setups (or whatever you call it when you say that it isn't okay to give a lonely answer with no justification). The silver lining is that this struggle forces me to think about WHY students should show work.  Here are a few reasons I have:

Showing steps . . .
Puts the focus on the process, rather than the solution.
Communicates your solution to others.
Makes it possible for you (or someone helping you) to locate your mistakes.
Slows you down, so fewer careless mistakes happen.
Gives evidence your answer is right.
Demonstrates your understanding.
Helps reduce cheating. (Some might still copy, but at least they must copy the work too.)
Finally, in my class an answer bank is given. Showing steps keeps practice from becoming nothing more than a matching game.

I am also asking myself some questions like . . . WHY do some students struggle with showing work?

Maybe because . . .
It takes too much time.
They can do it mentally.
They don't know how to show work.
They are bored.
They don't believe in its value.
They are cheating.

Writing this, I realized that when a student is repeatedly refusing to show their process, I tend to go straight to negative assumptions. I assume they are being stubborn and uncooperative, or that they must be cheating.

I am going to try to put the whole issue in a more positive light and see where the students are coming from. Maybe these students think that showing steps is just for the teacher's sake, and has no benefit to them personally.

Or, maybe they genuinely don't know how to express how they got the answer.

It also has me thinking about the types of questions I am asking. If someone can calculate the answer mentally, maybe the question wasn't challenging enough?

How do you motivate students to show their thoughts?

Detail: Today's Million Dollar Question

0 I Stopped Answering Questions

Not really . . . but I did stop using 10-15 minutes at the beginning of class to discuss and answer questions on the previous day's assignment.

Initially, it was an experiment. I felt like students weren't really invested in this time, and that most of them were falling into one of four categories:

1.  The procrastinators:  These students were using this time to finish the assignment.
2.  The ones who lacked perseverance:  These students would encounter a challenging problem and then stop working on it (or not even attempt it in the first place) because they could just "ask about it in class".
3.  The ones who were really engaged:  Most days, it felt like maybe 2 kids.
4.  The ones who were bored:  These students had the assignment finished and were ready to move on to  a new lesson.

So I stopped spending time on questions. (My students have answers, so they can check for correctness as they practice). And this is what happened:

1.  Most of the procrastinators found a time to finish the assignment before class.
2.  Many more students persevered through challenging problems because they didn't have the crutch of asking about it later.
3.  Many with legitimate questions would drop by before school to ask. Most of our students arrive 30 minutes before first bell, so this works well at our school.
4.  Most everyone started finishing the assignment outside of class.

These outcomes alone were enough for me to turn my experiment into a permanent routine, but there was another benefit that I wasn't expecting . . . I suddenly had an extra 10 - 15 minutes in every class period. What can you do with an extra 10 - 15 minutes?! Here's how I use the extra time:

I use a few bell work problems every day (I am testing out a new bell work strategy, more on that later) to review and check for understanding. If there are any major misconceptions, I can usually identify and address them during this time.

While teaching a new lesson, I have a lot more time for practice and checking for understanding. I still do a lot of talking, but I also do a lot of pausing while students try this or that and check with me (or a partner). I have time to work in several mini-formative checks, and address common misconceptions. The result is fewer issues on the practice/assignment, which in turn further reduces the need for the question/discussion time at the beginning of class the next day.

Sometimes I still wonder if I should bring back the question time, structured differently to eliminate the problems I was having. I haven't done this because I don't miss it. And neither do my students. I realized today that in 2 or 3 years, I haven't had a single student complain about why I don't answer questions at the beginning of class.

Detail: I Stopped Answering Questions

0 Missing the Point

Recently, I wrote about my system for assigning practice. I give students an answer bank with every assignment so that they can find mistakes and revise their work.

I know why I do it this way. The purpose of these assignments is practice, so I want to give them feedback while they are working. I want students to keep practicing until they are doing it correctly. I want them to learn from their mistakes.

We have only been in school for 8 days, but I have spent a lot of time trying to communicate this to students. I keep getting responses that tell me students don't really get it, like these:

1.  Extreme excitement, because having the answers feels like legalized cheating.
2.  Confusion (usually from the high achieving students), because they don't think it is fair that everyone has an equal chance of getting all the answers right.
3.  Resistance, from students who feel like it is pointless to show their process since they already know the answer.

Practice is a process, dear students! I will assess you soon, I promise.

I am not sure how I can help my precious Algebra 2 students to understand.

It seems obvious (but not all inclusive) to use some sort of sports analogy:  If you are learning a new football play and you totally mess it up, the coach doesn't mark a D- in the grade book and call it a day, does he? No, he doesn't. He sends you back out there to try it again until you get it right.

That is all I have for now . . . I am going to keep working on it.

Detail: Missing the Point

0 My Thoughts On Homework

Lately I have been thinking about how I assign, collect, and give points (or not) for homework. (For the record, when I say ‘homework’ I really mean ‘practice’. I want my students to practice every day. Sometimes they practice at home.)

I know a lot of bloggers have had success with not giving points for homework, but I am not ready to go there yet. I tried not giving points once during my first year of teaching and it was a disaster. Then again, lots of things during my first year of teaching were a disaster. But if giving students a score on a paper helps them to reflect on the quality of their efforts as they practice math, then I’m okay with using points.

So this is what I do . . . In bold is the thing I am trying to accomplish, and after that is how I attempt to make it happen.

1.     The perfect system emphasizes quality practice. Students need to reflect and make corrections as they are working:  I spend a lot of time teaching students how to practice. I want them to work out a problem, and then check the answer and find any mistakes and revise their work as needed. I hate to say just “show your work”. I do emphasize the importance of justifying your solution so that you can communicate to others how you found it, and prove it is correct. I make up a page of problems where some are perfect, others are missing work/justification, others have a wrong answer, and some have a right answer but the work/justification is incorrect or incomplete. Then students work with a partner to critique and discuss the quality of the practice. This takes time, but it is worth it.

2.     A good system gives students feedback while they are working, whether at home or at school. Ideally, they can find out if their answer is right or wrong without being told the actual correct answer: I put the answers to the problems in random order in the margin of the assignment. When students finish a problem, they find the answer in the margin and cross it out.  The only drawback here is that they can use the process of elimination to know the answer to the problems at the bottom of the page. Still, it works pretty well. I am thinking of tweaking this a little this year using the sum of a couple answers (sort of like Kate’s Add ‘em up). Instead of writing all the answers in the margin, I think I will try something like “the sum of #1 and #2 is _____”.  Then they will know if they need to fix their work without giving away any answers.

3.     If points are given, the points should reflect the quality of the practice vs. the number of answers that are correct on the first try:  A problem counts for points if it has correct work (or justification of some kind) leading to the correct answer, regardless of how many tries it takes you to get there. I don’t really even think of it as a “homework” grade. I want the point value to help students think about how well they are practicing. Hmm, maybe I will start calling it the “quality of practice” grade. Or something like that . . . I will have to think of something more catchy.

4.    If points are given, the system minimizes teacher time spent grading and recording:  My students spend so much time learning what good practice looks like that they know whether a problem they have finished qualifies. It has correct work leading to the correct answer and it counts, or it doesn’t. So students take the number of problems that qualify as good practice divided by the total number of problems times 5 (because I want a practice assignment with 20 short problems to have the same value as a practice assignment with 4 or 5 lengthy ones). I will even put that formula at the top of the paper to make it simple. Round the number to the nearest tenth and hand it in. Teacher records that number.

I am pretty happy with this system, but I still have a few problems. Sometimes students put a score on their paper that isn’t accurate (pretty easy to catch). Sometimes students rely too heavily on clues from the answers in the margin (maybe my little tweak will help that). Sometimes students copy their friend’s homework in the hallway before school (but at least they have to copy the work, too).

What's your homework system?

Detail: My Thoughts On Homework