Saturday, August 20, 2011

One last plank in the HW plan

Oh, yeah. A problem that I always had last year was with assigning homework in advance. I was assigning work from the day's lesson, as more practice. The problem was that I had trouble assigning work in advance, since I never knew in advance how much or what I was going to cover. And I had to make print outs in advance. but what I'll do this year is stagger the homework so that it's more practice on things that we've already done in class.

I came across this (in retrospect, fairly straightforward) idea when reading this awesome piece from Henri Piciotto.

I like this because it gets at two of my problems at once: my organization and clarity issue, and my retention issue.

Tuesday, August 16, 2011

The 703rd Homework Plan Posted by a Math teacher

Seriously, homework is a pain in the neck for everyone. But here's what I'm going to do this year, I think.

Why don't you just give me the summary at the beginning of the post, instead of the end?


1. Accountability, moderately tied to grades, with open-notebook homework quizzes. You've seen these before from Sam and Kate.
2. Instead of handouts and worksheets, students get a link to a site with questions, answers and explanations. I happen to like
3. We don't spend a ton of class going over homework, but I do start the day with a Warm Up exercise with some problems that are pretty similar to homework.

Ok. Now, the details.

A. Students get a link to an online problem set: The problem set has solutions and explanations. Students are assigned some problems and are expected to answer the problems fully in a separate homework notebook.

B. I've got three students: Rachel, Jimmy, and John.

Rachel already knows how to do this stuff, and doesn't think that she needs the practice. She doesn't do the homework.

Jimmy doesn't know how to do this stuff, so he tries a problem. It's wrong -- the site tells him that -- and so he clicks around until he finds the right answer. Then he reads the explanation. He copies this into his notebook. Then he tries another, similar question. The hope is, now Jimmy might as well try it again, and he gets it right.

John doesn't know how to do this stuff, and John doesn't do the homework.

C. A couple times a week I spend 5 minutes at the end of class giving a HW quiz. The HW quiz can be on ANYTHING that has been assigned for homework since the beginning of the year. They're allowed to use their homework notebooks, and I tell them the date-assigned and number of the questions on the quiz.
Rachel does fine, since she knows the material. (Or she doesn't, and she realizes that maybe she needs more practice.)

Jimmy does fine, since he has his homework notebook to help. He sees the problem for another time, which is helpful for Jimmy.

John doesn't do well on the homework quiz. I try to figure out why, and then I try to help John.

D. I could even build in some meta-cognition into the homework quiz. Maybe, for each question, they're asked "Could I do this without my homework notebook?"

We'll see how this goes, but I'm more confident with this plan than with my non-plan from last year.

Thursday, August 4, 2011

[WDIDWT] Short Student Conversations

"Now, with your partner to your left..."

I found it confusing to just talk about "group work." Group work can mean a bunch of different things. For this edition of "When do I do (with) this?" I want to talk about an especially structured, baby-step flavor of collaborative learning. In this sort of instruction the teacher is not helping students learn by explaining something. Rather, students are having conversations with each other. They're usually assigned a single task, and are assigned a partner to work out the task with.

For example, one structure for this type of instruction is "Think-Pair-Share." Here's a description of how this works:

In think-pair-share, the instructor poses a challenging or open-ended question and gives students a half to one minute to think about the question. (This is important because it gives students a chance to start to formulate answers by retrieving information from long-term memory.) Students then pair with a collaborative group member or neighbor sitting nearby and discuss their ideas about the question for several minutes. (The instructor may wish to always have students pair with a non-collaborative group member to expose them to more learning styles.) The think-pair-share structure gives all students the opportunity to discuss their ideas. This is important because students start to construct their knowledge in these discussions and also to find out what they do and do not know. This active process is not normally available to them during traditional lectures. (Source: National Institute for Science Education)
Why would I do this?

A bunch of reasons.

First, because the brain needs processing time. Here's a quote from Teaching with the Brain in Mind:
Alcino Silva discovered that mice improved their learning with short training sessions punctuated by rest intervals. He says that the rest time allows the brain to recycle CREB, an  acronym for a protein switch crucial to long-term memory formation...This asociation and consolidation process can only occur during down time, says Allan Hobson of Harvard University.
The same thing is pretty much summarized here.

Another reason for using this instructional strategy is that you can use it to get students to actively engage with a concept that they might have only previously had a surface acquaintance with. A good question is important here, such as "Show me an example" or "What's the difference between..."

It also provides students an opportunity to evaluate their understanding, since they're faced with a partner who has a different understanding than they do. 

When do I do this? 

Do this when students have just encountered a new idea, or you've lectured for 10-15 minutes, because your students need
(1) processing time
(2) a more active learning style
(3) an opportunity for self-assessment.

Here are some ways to vary this activity. I'll add more as I find them.
* Think-Pair-Share
* Mini-quiz
* Quickwrites


This should be part of the every day routine and part of the planning process. It's also a good mini-step into group work. For me, the progression is something like:
Level 1: Short Student Conversations (Pairs)
Level 2: Longer Student Conversations (Pairs)
Level 3: Longer Student Conversations (Larger groups)
Level 4: Group problem-solving

My hope is to start off the year at Level 1, and only ascend when I feel totally in control of the previous levels.

Tuesday, August 2, 2011

[WDIDWT] When do I do with this? Lecture Edition


Folks, it's a joke. Just ignore it and move on to the post.

I'm hoping that this will be the first in a series. One of the things that I'm struggling with right now is that I don't have a good sense for when the various instructional strategies are appropriate.

When do I lecture?
When do I have students explain ideas to each other?
When do I assign a worksheet?
When do I have students solving an application problem?
When do I question with the entire class?
When do I have the class look for procedural mistakes?

Feel very, very free to leave your thoughts in the comments.

I'm going to start with lectures, since it's what I spend most of my time doing in the classroom. (Scorn! Scorn!)

 First, though, I suppose we should define what it means to lecture. For various reasons (explained here), I think that it's helpful to take the word "lecture" to essentially mean "explaining." I take lecturing to be a specific flavor of explaining -- lecturing to me is explaining something to a larger audience. Clearly, sometimes explaining is a good way to help a person learn new information. After all, we spend much of our communication with others explaining things. The question is, how should it work in the classroom?

When should I lecture?

Here's a neat little summary of some papers that I found on a neat little website:

Johnson, et. al (1991) and Bonwell and Eison (1991) highlight several uses where lectures are appropriate:
  • To disseminate information to a large number of people in a short period of time.
  • To present concepts too difficult for students to process on their own.
  • To gather information from a variety of sources that may take the students a long time to gather.
  • To arose interest in the subject.
  • To teach auditory learners.
  • To present information unavailable to the public such as original research. 

This list rings true with me. But even when lecture is appropriate, it needs to be used carefully.
"Research shows that students listening to a 50-60 minute lecture are unable psychologically or physiologically to concentrate on the content and retain it. One study found students could recall 70% of the content from the first 10 minutes of the lecture but only 20% from the last 10 minutes (Hartley and Davies, 1986)"
Lesson: don't lecture for long. Combine that with the unique capacity of verbal communication to inspire and captivate, and there's a strong case for starting each lesson with a short lecture that does some of the following things:
1. Motivates the content.
2. Provides necessary background information.
3. Takes a first pass at explaining a concept.

The trickiest thing is the third, though. A lecture should hit as many people as possible with a concept, but it's crucial that students not feel as if they understand the entire concept from the lecture. This is a subtle thing, but if you lead off with an explanation, that's going to feel like learning to the student, and make it harder to follow up with instructions that aims to deepen that knowledge. That's probably more something to be aware of for introducing those sorts of activities, rather than lecture, though. Lecture can't be the whole story, but there's no reason to force it to do less than it's capable of. That's just being silly.


In summary:
1. Lectures are good at arousing interest in a subject. It's good to lead with that.
2. No reason not to try to hit as many people with the hard/essential/fundamental concept of the day with the lecture. Just make sure that you follow that up with an activity that takes a second pass at this concept, and make sure that you don't allow students to convince themselves that lecture gave them all that they need. (Try, asking a question whose answer is a straightforward, but unintuitive, consequence of the new concept).
3. Don't lecture for long without breaking it up with some sort of pause procedure.

Sources: (will hopefully update this as I discover more sources)

Monday, August 1, 2011

How I want to spend my August

It's only a month until school starts up again, and I want to be ruthlessly efficient in these next few weeks. So I need to spend some time clarifying what I need to do in order to get ready for school. So, here's my list of things that I need to get done.

(0. Various side projects and relaxing. I haven't forgotten these at all.)

1. Homework -- I need to figure out how it's going to be assigned and assessed. I didn't grade it at all last year, and students didn't do it, so I stopped bothering to assign it, essentially. I need to choose some sort of structure to at least start things off with. I'm leaning towards bi-weekly homework quizzes, and 4-8 problems assigned nightly. I've also been playing around with the idea of reading assignments.

2. Grading -- My big question is will I grade behavior, and (if I do) how will I grade behavior? Also, need to figure out where homework and classwork fit into here. Also also, I'm hoping to do skills quizzes and also summative tests, so I need to figure out how that will work. I also need to set up my gradebook before school starts, as there were aspects of my set up last year that made it hard for me to make changes. (Can Google please develop a free product aimed at schools so that I can just use GoogleDocs, puh-lease? I need something that integrates well with Excel, at the very least.)

3. Ice Cream -- Eat ice cream. Lots and lots of ice cream. This is going great.

4. Skills quizzes -- I need to finalize my skills lists, enter them into the gradebook for the kids, and figure out how I'm going to work on retention this year. Also, I like the idea of grading being dynamic both for better and for worse, but I'm not sure how to work that out. Maybe by adding the two scores? Maybe by making the first time they see the skill worth one point, and the second time worth 4? And when exactly am I going to give these skill quizzes -- weekly? When we finish a topic? (Last year I just did a skill quiz when we finished a topic, but that didn't allow for retention checks since we were already asking pretty time-consuming questions.)

5. Small-group work -- I want to implement some small group work into my classes in a more formal, regular way, but I'm not sure how or where to start. I'd like for it to be a regular, structured feature of learning in my classroom.

6. Blend -- So I bought a blender. Ideas on things to blend? Everything I've made so far has just been good, not great. I'm aiming for greatness, immortality, milkshakes, etc.

7. Good questions and important points -- I want to start compiling a list of good questions to ask students for my different units, as well as compiling a list of the hard parts that my students struggle with. I think that this is the best sort of prep that I can do, in terms of lesson planning. It'll make me more efficient over the course of the semester. This, rather than compiling activities, seems to be a good use of my time. It will also make it easier for me to lay bare the connections between different topics.

8. Binders -- Plan on how I'm going to use binders with students. I think that there should be dividers for things such as calculator instructions, a different divider for notes, a different divider for handouts, and a folder for their quizzes/tests. Then they should also have a list of the skills that they need to know. I'd like to make a model binder for myself.

9. Buy a stapler. I often need to staple things.

10. Don't blog when I'm hungry. This is really just a note for myself, but, man, I'm really hungry. I'm going to go blend something.

How the elephant got its lifespan.

[Insert adorable elephant photo.]

This post is about a linear regression lesson. Nothing Earth-shattering, but something to add to the list of data to analyze. In short: here is some data that is pretty linear, and the relationship is graspable by students. But since the data is only pretty linear, it forces us to have a discussion about outliers, error-bars and correlation coefficient. So, better to use data that is only sort of linear (r = +/- 0.6 sounds right) for linear regression.

First, some facts:

* An opossum pregnancy lasts about 15 days, and their children live for about a year.
* Dogs spend about 60 days gestating, and they can expect to live for 10 years.
* Elephants spend, on average, 624 days in the womb.

When I consider these three facts, I find myself really bugged by one question – how long does the elephant live?

The first thing we need is more info about the relationship between gestation and birth.

After that, we need to figure out a way of representing this info in a clean and easy to read way. Then we want to see if we can figure out any pattern that would help us predict how long an animal will live, depending on gestation period.

Here we hit a problem: There does seem to be a general tendency for animals to live longer when they spend more time gestating. But there’s no perfect pattern here. Some animals seem to fit the pattern, while others don’t.

And this is what many of my students find confusing about statistics. They’re used to dealing with perfect patterns and absolute relationships, but what do we do with half-patterns and tendencies?

We make an educated guess, and make sure that we are clear about how much we’re guessing. We make a guess, in this case, by drawing a line that more-or-less passes through the data points.

So what about elephants? If this line correctly describes the pattern, then we would expect elephants to live for about 40 years, on average. As it turns out, the average elephant lifespan is 40 years. In this case, at least, the guess is right on.