Maria Anderson summarizes the various approaches to teaching found in most undergraduate math classes:
Math Instruction Practices
Tuesday, September 22, 2015
Friday, September 18, 2015
A Busy Professor's Guide to Sanely Flipping Your Class - Dr. Cynthia Furse
Some great thoughts on why and how to flip. First-hand experiences shared and key experiences given.
Video
Video
First the Theory
Returning to the cheesemonkeysf summation of How People Learn: Brain, Mind, Experience, and School now with a discussion of the four stages being advocated.
The stages (as summarized by cheesemonkeysf) are:
(Now isn't that a pretty copy and paste from THIS post?)
I would like to flesh out some of these ideas, highlight some of the language that is meaningful, and then explore how this might look in a REAL classroom. This post will be the "fleshing out" post. Let's start with Stage 1.
Stage 1 - Students arrive in class rarely ready to engage with the material. Their minds are elsewhere (probably Facebook) and they don't switch their thinking quickly. This is the reality of education. As a result, something needs to be done to help students switch from "whatever the heck a teenager/student/working adult" thinks about to the topic at hand.
There are at least two components to helping students make this switch when they enter your classroom: 1) a successful introductory task and 2) consistency.
Something needs to be done to get the students' attention. A task, a video, a question, a discussion, a story, something. Perhaps the task is related to the material for the day and perhaps it isn't (more on this later) but something needs to be done BEFORE you can start teaching. If the task isn't directly related to the content of the day there should be something about it that asks them to think and move into an academic mindset.
More of cheesemonkeysf's commentary on Stage 1:
STAGE 1
A good discovery activity can be a powerful catalyst for learning in Stage 1. But unfortunately, sometimes there just really isn't a great discovery activity that leads students captivatingly but inexorably to a blinding insight that will transform their learning forever.
Sometimes the best you've got is a mediocre discovery activity from a textbook that kinda sorta leads students in the general direction — but not without a lot of heavy-handed guidance. Or perhaps there is some other deficiency in what is available to you.
Like Gattegno, I believe that all learners have an energy "budget," and that means I have to make savvy and strategic decisions about how I'm going to ask my students to apply theirs. A boring or mediocre discovery activity can take just as much energy as a great one, but without the payoff of leaving students energized.
So sometimes I've learned I have to ask myself, is a discovery activity thebest choice I can make here at Stage 1? Or do I have some other kind of introductory task I could use — such as a simulation, a story, a funny or interesting deleted scene, or some other kind of analogy — that will get my class into the learning episode faster and free up more of their energies to developing the necessary fluency that a rich and interesting transfer task may require?
To me, the most important thing that can happen in Stage 1 of a learning episode is that students come sharply to appreciate the Burning Question of this segment. Whenever possible, I really like for my students to arrive at a Burning Question through a collaborative discovery activity that they own because when they own it, they buy into it.
But realistically, this is simply not always possible with every single topic in the curriculum. So I have a range of strategies for Stage 1 that can get my students to a Burning Question even though there may be a gap in my pedagogical arsenal.
Key phrases for further consideration and exploration - "catalyst for learning", may not be an activity to is captivating, "energy budget", a mediocre activity may only be just as good as a bad activity, perhaps there are other activities that will get the class into the "learning episode" and save energy for other necessary activities, "students come sharply to appreciate the Burning Question", "uncover and organize prior knowledge", "provide occasion for exploratory talk", "not always possible with every single topic", have a range of strategies that can get student to a Burning Question.
The stages (as summarized by cheesemonkeysf) are:
STAGE 1 - a hands-on introductory task designed to uncover & organize prior knowledge. In this stage, collaborative activity provides an occasion for exploratory talk so that students can uncover and begin to organize their existing knowledge;
STAGE 2 - initial provision of a new expert model, with scaffolding & metacognitive practices woven together. The goal here is to help students bring their new ideas and knowledge into clearer focus so that they can reach the next level. Here again, collaborative activity can provide a setting in which to externalize mental processes and to negotiate understanding, although often, this can be a good place to offer some direct instruction;
STAGE 3 - what HPL refers to as "'deliberate practice' with metacognitive self-monitoring." Here the idea is to use cooperative learning structures to create a place of practice in which learners can work within a clearly defined structure in which they can advance through the 3 stages of fluency (effortful -> relatively effortless -> automatic)
STAGE 4 - working through a transfer task (or tasks) to apply and extend their new knowledge in new and non-routine contexts.
(Now isn't that a pretty copy and paste from THIS post?)
I would like to flesh out some of these ideas, highlight some of the language that is meaningful, and then explore how this might look in a REAL classroom. This post will be the "fleshing out" post. Let's start with Stage 1.
Stage 1 - Students arrive in class rarely ready to engage with the material. Their minds are elsewhere (probably Facebook) and they don't switch their thinking quickly. This is the reality of education. As a result, something needs to be done to help students switch from "whatever the heck a teenager/student/working adult" thinks about to the topic at hand.
There are at least two components to helping students make this switch when they enter your classroom: 1) a successful introductory task and 2) consistency.
Something needs to be done to get the students' attention. A task, a video, a question, a discussion, a story, something. Perhaps the task is related to the material for the day and perhaps it isn't (more on this later) but something needs to be done BEFORE you can start teaching. If the task isn't directly related to the content of the day there should be something about it that asks them to think and move into an academic mindset.
More of cheesemonkeysf's commentary on Stage 1:
STAGE 1
A good discovery activity can be a powerful catalyst for learning in Stage 1. But unfortunately, sometimes there just really isn't a great discovery activity that leads students captivatingly but inexorably to a blinding insight that will transform their learning forever.
Sometimes the best you've got is a mediocre discovery activity from a textbook that kinda sorta leads students in the general direction — but not without a lot of heavy-handed guidance. Or perhaps there is some other deficiency in what is available to you.
Like Gattegno, I believe that all learners have an energy "budget," and that means I have to make savvy and strategic decisions about how I'm going to ask my students to apply theirs. A boring or mediocre discovery activity can take just as much energy as a great one, but without the payoff of leaving students energized.
So sometimes I've learned I have to ask myself, is a discovery activity thebest choice I can make here at Stage 1? Or do I have some other kind of introductory task I could use — such as a simulation, a story, a funny or interesting deleted scene, or some other kind of analogy — that will get my class into the learning episode faster and free up more of their energies to developing the necessary fluency that a rich and interesting transfer task may require?
To me, the most important thing that can happen in Stage 1 of a learning episode is that students come sharply to appreciate the Burning Question of this segment. Whenever possible, I really like for my students to arrive at a Burning Question through a collaborative discovery activity that they own because when they own it, they buy into it.
But realistically, this is simply not always possible with every single topic in the curriculum. So I have a range of strategies for Stage 1 that can get my students to a Burning Question even though there may be a gap in my pedagogical arsenal.
Key phrases for further consideration and exploration - "catalyst for learning", may not be an activity to is captivating, "energy budget", a mediocre activity may only be just as good as a bad activity, perhaps there are other activities that will get the class into the "learning episode" and save energy for other necessary activities, "students come sharply to appreciate the Burning Question", "uncover and organize prior knowledge", "provide occasion for exploratory talk", "not always possible with every single topic", have a range of strategies that can get student to a Burning Question.
Wednesday, September 16, 2015
First Day Activity and Discussion - Maze Moments
This might be an appropriate thing to do on the first day of class. Solve mazes, discuss problem solving strategies, and relate all of that to solving math problems.
Maze Moments
Maze Moments
How People Learn
cheesmonkeysf (I assume this is not her real name.) provides a great summary of "How People Learn" in this post:
"How People Learn" and how people learn
"How People Learn" and how people learn
Choosing a Teaching Approach
It takes about 2 seconds in the teaching profession before you start asking yourself "Should I be doing something different?" Now, don't think I'm talking about the desire for a different career choice. Perhaps the more accurate question is "Should I be doing something different in the classroom?"
There are many reasons we are constantly assailed by this question as teachers: the desire to be more effective; the frustration of seeing students fail or show only minimal signs of life; administrators signing up for new programs; or the constant barrage of new ideas about teaching that are always being advocated.
So what is a teacher to day? Here are some suggestions purely from my own experience and lacking any sort of reference.
1. Play to your strengths. If you do something well that no one else does then make sure your plan always includes that strength.
2. Don't feel the need to be original. Some teachers feel like unless they are using a method that they developed themselves then they really aren't teaching. Not true. It is perfectly fine to use materials, ideas, philosophies, etc. that have already been created or developed. Using these already-existing materials allows you to free up more time to do things YOU are good at.
3. Develop the ability to ignore ideas. Not everything (even the great ideas) you discover can or should be implemented in your classes. It's okay to say "Wow, that's a great idea! But I am not going to use it because I am doing something else." It's not necessary (and clearly it is impossible) to use all of the great ideas that are out there.
4. Put your own twist on things. If you find a good idea you want to use accept the fact that you will need to change the idea in some way to work for you. Your personal and classroom circumstances will almost always be different that those of the creator of the idea. It's just fine to take an idea and implement only a small portion of it that fits. Nothing is set in stone.
5. Enjoy and value what you do do (hee-hee) in class. There has never been nor will there ever be a perfect class. Saying to yourself "when I get this approach mastered or when I have totally polished this lesson plan, then I will feel like I am effective" is a first step to burn-out and frustration. Each and every day, whether you feel 100% prepared or not, you get the chance to talk about a topic you enjoy and spend some time with students who you care about. That's a pretty good day job. Enjoy it and don't wait for things to be perfect to do so.
6. Never make a list with more than 5 items.
These are just some thoughts I've had and perhaps will find some literature on the topic for the future.
There are many reasons we are constantly assailed by this question as teachers: the desire to be more effective; the frustration of seeing students fail or show only minimal signs of life; administrators signing up for new programs; or the constant barrage of new ideas about teaching that are always being advocated.
So what is a teacher to day? Here are some suggestions purely from my own experience and lacking any sort of reference.
1. Play to your strengths. If you do something well that no one else does then make sure your plan always includes that strength.
2. Don't feel the need to be original. Some teachers feel like unless they are using a method that they developed themselves then they really aren't teaching. Not true. It is perfectly fine to use materials, ideas, philosophies, etc. that have already been created or developed. Using these already-existing materials allows you to free up more time to do things YOU are good at.
3. Develop the ability to ignore ideas. Not everything (even the great ideas) you discover can or should be implemented in your classes. It's okay to say "Wow, that's a great idea! But I am not going to use it because I am doing something else." It's not necessary (and clearly it is impossible) to use all of the great ideas that are out there.
4. Put your own twist on things. If you find a good idea you want to use accept the fact that you will need to change the idea in some way to work for you. Your personal and classroom circumstances will almost always be different that those of the creator of the idea. It's just fine to take an idea and implement only a small portion of it that fits. Nothing is set in stone.
5. Enjoy and value what you do do (hee-hee) in class. There has never been nor will there ever be a perfect class. Saying to yourself "when I get this approach mastered or when I have totally polished this lesson plan, then I will feel like I am effective" is a first step to burn-out and frustration. Each and every day, whether you feel 100% prepared or not, you get the chance to talk about a topic you enjoy and spend some time with students who you care about. That's a pretty good day job. Enjoy it and don't wait for things to be perfect to do so.
6. Never make a list with more than 5 items.
These are just some thoughts I've had and perhaps will find some literature on the topic for the future.
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