Archive for the ‘Book Notes/Ideas’ Category
I’m swiping this from Matt Townsley:
Each Learning Target is scored using a 4-point scale:
4 – demonstrates thorough understanding
3.5 – high level of understanding, but with small errors
3 – demonstrates understanding, but with significant gaps
2 – shows some understanding, but insufficient for a passing grade
1 – Attempts the problem
He’s also got a post I’m interested in on how to explain all this to parents.
According to Never Work Harder Than Your Students, any teacher can become a master teacher by applying 7 basic principles:
- Master teachers start where their students are.
- Master teachers know where their students are going.
- Master teachers expect to get their students to their goal.
- Master teachers support their students along the way.
- Master teachers use feedback to help them and their students get better.
- Master teachers focus on quality rather than quantity.
- Master teachers never work harder than their students.
When I took the pretest, I scored a total of 138 — just on the beginning edge of “Practitioner”, but most of my average scores on each principle were between 2 and 3. According to the book, I now need to set up an Action Plan to address those principles whose scores were closest to 3, which are principles 3, 5, and 6. Since I am supposed to start with one principle at a time, I will start with 3: Master teachers expect to get their students to their goal.
The action plan is divided into eight parts:
- Identify the Principle I will work to develop and conduct an analysis of how I have been applying the principle to my practice so far.
- Use the Getting Started steps to to help figure out what specific steps I will need to take in order to improve my practice of the principle.
- Detail what Specific Actions I will take in order to apply each Getting Started step to my own teaching.
- Decide what feedback (Evidence) I will collect to tell whether I am making progress.
- Identify any Resources I will need to implement the action steps.
- Identify a Due Date for when I will implement each step.
- Anticipate any Obstacles I may face along the way.
- Think about how I will Monitor my progress and when my Completion Date will be.
Some ideas I had from reading The Life of Fred: Fractions:
- The notes should include several circles that students can practice dividing into fourths, sixths, etc.
- Also use the notes so that they can color in shapes to see equivalent fractions.
- Practice filling in “ruler” fractions (1/8, 1/4, 3/8, etc.)
- Dividing three pizzas between eight people
- Use commutative property to show how to cancel when multiplying.
- Use “opposites” to show why dividing by a fraction is the same as flipping and multiplying.
- Include dimensional analysis as part of multiplying fractions.
As a simple model for how our minds work, we have our “working memory”, which holds the stuff we are currently thinking about, and “long-term memory”, which is the storehouse of all of the factual knowledge we have about the world, both concrete and abstract.
All of the information in long-term memory resides outside of awareness. It lies quietly until it is needed, and then enters working memory and so becomes conscious. For example, if I asked you, “What color is a polar bear?” you would say, “white” almost immediately. That information was in long-term memory thirty seconds ago, but you weren’t aware of it until I posed the question that made it relevant to ongoing thought, whereupon it entered working memory.
When we combine information from our environment and long-term memory in new ways, thinking occurs. This combining happens in our working memory. How we approach solving problems, and how easily we solve them, depends on the information stored in our long-term memory. For instance, if we are given a puzzle to solve that we have not seen before, we have to use our working memory almost exclusively, both to take information from our environment–the rules and configuration of the puzzle–but also to imagine the moves to solve the puzzle. By contrast, if we have seen the puzzle before, already have information in our long-term memory about how to solve it, even if that is not foolproof.
Another example is to consider multiplying two numbers, such as 18 and 7. Not only does our long-term memory contain factual knowledge, it also contains what could be called “procedural knowledge”, which is our knowledge of the mental procedures necessary to execute tasks.
If thinking is combining information in working memory, then procedural knowledge is a list of what to combine and when–it’s like a recipe to accomplish a particular type of thought.
In sum, successful thinking relies on four factors:
- information from the environment
- facts in long-term memory
- procedures in long-term memory
- the amount of space in working memory
If any one of these factors is inadequate, thinking will likely fail.
The author suggests seven implications for teachers from this information:
- Be sure that there are problems to be solved — that is, cognitive work that poses a moderate challenge, and be sure that
- students understand what they are to do,
- students are likely to be able to solve the problem, and
- students will not simply guess what we would like them to say or do.
- Respect students’ cognitive limits — make sure students have enough background knowledge to solve the problem, and do not overload their working memories. Overloads can be caused by
- multistep instructions
- lists of unconnected facts
- chains of logic more than two or three steps long
- the application of a just-learned concept to new material (unless the concept is quite simple)
- Clarifying the problems to be solved — in order to engage students, it’s important to spend some time developing the key questions for that lesson that need to be answered.
- Reconsider when to puzzle students — if an introductory demonstration is like a magic trick, it will be a momentary thrill, but the students’ curiosity to understand may not be long-lasting if they don’t have sufficient background knowledge.
- Accept and act on variation in student preparation — giving students work that is beyond them is unlikely to help them catch up, and is likely to make them fall still further behind.
- Change the pace — plan shifts and monitor the class’s attention.
- Keep a diary — make a habit of recording what works and what doesn’t.
I found this pretty fascinating:
Contrary to popular belief, the brain is not designed for thinking. It’s designed to save you from having to think, because the brain is actually not very goot at thinking. Thinking is slow and unreliable. People like to solve problems, but not to work on unsolvable problems.
Humans are good at certain typese of reasoning, particularly in comparison to other animals, but we exercise those abilities infrequently. Your brain serves many purposes, and thinking is not the one it serves best. Your brain also supports the ability to see and to move, for example, and these functions operate much more efficiently and reliably than your ability to think. It’s not accident that most of your brain’s real estate is devoted to these activities. The extra brain power is needed because seeing is actually more difficult than playing chess or solving calculus problems.
Five dollars will get you a calculator that can perform simple calculations faster and more accurately than any human can. With fifty dollars you can buy chess software that can defeat more than 99 percent of the world’s population. But the most powerful computer on the planet can’t drive a truck. Tasks that you take for granted–for example, walking on a rocky shore where the footing is uncertain–are much more difficult than playing top-level chess. No computer can do it.
According to the author, thinking is slow, effortful, and uncertain, especially compared with our visual system. We do not have to analyze what we see–we take in the whole scene, completely, and without really concentrating on it. If we make a mistake in something we see, we are usually not that far off, unlike what can happen trying to solve a problem. If thinking is such hard work, then, how do we cope? The author’s answer is that when we can get away with it, we don’t actually think at all–we rely on memory.
Most of the problems we face are ones we’ve solved before, so we just do what we’ve done in the past. Just as your visual system takes in a scene and, without any effort on your part, tells you what is in the environment, so too your memory system immediately and effortlessly recognizes that you’ve heard the problem before and provides the answer. You may think you have a terrible memory, and it’s true that your memory system is not as reliable as your visual or movement system–sometimes you forget, sometimes you think you remember when you don’t–but your memory system is much more reliable than your thinking system, and it provides answers quickly and with little effort. For the vast majority of decisions we make, we don’t stop to consider what we might do, reason about it, anticipate possible consequences, and so on. When you feel as though you are “on autopilot,” even if you’re doing something rather complex, such as driving home from school, it’s because you are using memory to guide your behavior. Using memory doesn’t require much of your attention, so you are free to daydream, even as you’re stopping at red lights, passing cars, watching for pedestrians, and so on.
You are biased to use memory to guide your actions rather than to think. But your brain doesn’t leave it there; it is capable of changing in order to save you from having to think. If you repeat the same thought-demanding task againi and again, it will eventually become automatic; your brain will change so that you can complete the task without thinking about it.
The implications for education sound rather grim. If people are bad at thinking and try to avoid it, what does that say about students’ attitudes toward school? Fortunately, the story doesn’t end with people stubbornly refusing to think. Despite the fact that we’re not that good at it, we actually like to think. We are naturally curious, and we look for opportunities to engage in certain types of thought. But because thinking is so hard, the conditions have to be right for this curiousity to thrive, or we quit thinking rather readily.
When you solve a problem, your brain may reward itself with a small dose of dopamine, a naturally occurring chemical that is important to the brain’s pleasure system. It’s notable too that the pleasure is in the solving of the problem. Working on a problem with no sense that you’re making progress is not pleasurable. In fact, it’s frustrating. Then too, there’s not great pleasure in simply knowing [or being told] the answer. Even if someone doesn’t tell you the answer to a problem, once you’ve had too many hints you lose the sense that you’ve solved the problem, and getting the answer doesn’t bring the same mental snap of satisfaction.
Mental work appeals to us because it offers the opportunity for that pleasant feeling when it succeeds. But not all types of thinking are equally attractive. We are curious about some stuff but not about other stuff, [b]ut I don’t think content drives interest. The answer may lie in the difficulty of the problem. If we get a little burst of pleasure from solving a problem, then there’s no point in working on a problem that is too easy–there’ll be no pleasure when it’s solved because it didn’t feel like much of a problem in the first place. Then too, when you size up a problem as very difficult, you are judging that you’re unlikely to solve it, and are therefore unlikely to get the satisfaction that comes with the solution.
This analysis of the sorts of mental work that people seek out or avoid also provides one answer to why more students don’t like school. Working on problems that are of the right level of difficulty is rewarding, but working on problems that are too easy or too difficult is unpleasant. Students can’t opt out of these problems the way adults often can. If the student routinely gets work that is a bit too difficult, it’s little wonder that he doesn’t care much for school.
So what’s the solution? Give the student easier work? You could, but of course you’d have to be careful not to make it so easy that the student would be bored. Andy anyway, wouldn’t it be better to boost the student’s ability a little bit? Instead of making the work easier, is it possible to make thinking easier?
- Instead of just posting the section name, also post the objective(s) for that day’s lesson.
- Give each student a pretest to see how well-prepared they are. This can include ideas and topics they would not have seen yet; at the end of the semester, give it to them again, so they (and I) can see how much they have improved.
- Reverse roleplay interrupting someone who is speaking.