My 2nd Session (Thursday) was done by Susan May and Kathi Cook from the Charles A. Dana Center at the University of Texas (Austin). I also met up with @Fouss and @Sarah_IC - all three of us had it on our list. I chose this one because I have lower level students who do struggle and I don't want them to give up so easily.
Website with more information - in progress, presentation and handouts will be there eventually.
The first part of the session was spent talking about what persistence is, what characteristics persistent students have and the importance of it. The second part of the session was talking about some of the mechanics (for lack of a better word) of how to get there.
Bascially, they chose to focus on Algebra 1 because it is the course that creates the greatest angst - there are two transitions occurring at that time: the transition from Middle School to High School and the transition from K-8 Math to math that has an algebraic focus.
Persistent students -
**understand the role of challenging tasks in learning
**understand that setbacks can be a natural part of learning
**engage in self-monitoring
**learn from setbacks and struggles
Persistence is related to what you're doing.
They talked about the theories of Carol Dweck (views of intellegence - fixed vs. malleable) and Barry Zimmerman (self-regulated learning theory). These theories shaped quite a bit of their work.
Why do we want to persistent learn?
**The problems get bigger.
Think of a time outside of school where you struggled. Then think of the satisfaction when you get through the struggle. This was how they framed why persistence is important.
As students are working through the problems, they have 2 tools - a Problem-Solving Tool and a self-reflection tool. The problem solving tool has the four steps outlined with key questions - make a plan, monitor work, evaluate, and loop back. The idea is that students are jotting down their thoughts as they work through the problem. Then, once they are finished, they complete the self-reflection tool, which is a series of questions about how the process went.
As you are working through introducing the process to students, you start with smaller, easier problems first (the bucket problem from Die Hard for example). You should be modeling what the thoughts of a persistent student are and introduce the inner dialogue to them. You have to step students into this process. Help students to learn how to reflect and understand that it's not just about the answer. There is a delicate balance between productive struggle and frustration.
This whole process takes time. The suggestion was to set aside a day each week to work on the problems in class (for example, Fridays). Students can work on the problems outside of class, but only that day will be devoted to class time on the problems. They suggested the NOYCE Foundation Problems of the Month, which have 5 levels to the problems. This way, all students can find somewhere to start, but also will reach a point where they struggle. It doesn't matter where the kids get with the problem (Level A, Level E, etc.), but it matters that they are struggling. Every student is working at the place they are at. It's important to make srue they are reflecting. The ultimate goal is that every time they are working on challenging problems students are asking themselves the reflective questions.
Two other websites they provided:
Academic Youth Development
Neuroscience for Kids
I really liked this session. I am still struggling with the how to make the Rich Problem thing work and for the first time, I felt like I had an answer on how to start. I definitely want to incorporate this in my classes next year. This will be a definitely project to pursue this summer. I am also considering incorporating this into my Math 1 classes for the rest of the year just to see how it goes. Haven't decided if I'm going to for sure, but I am thinking about it. Good session - check out the websites.
Showing posts with label Rich Problems. Show all posts
Showing posts with label Rich Problems. Show all posts
Thursday, April 14, 2011
NCTM11 - Teaching for Reasoning and Sense Making
The first session I attended at NCTM was "Teaching for Reasoning and Sense Making: How Does it Work?" and Fred Dillon, Jenny Salls, and Christine Thomas were the presenters. I have seen Fred Dillon before and that was part of the reason I chose the session. The other reason I chose it was because the title intrigued me. The pdf of the slides for this session can be found here.
Basically what reasoning and sense making does is puts the mathematical skills into practice. It fits right in with Race to the Top and the Common Core practices. I think I remember Fred saying that this really fits in with the first one on the list.
We proceeded to work through a problem about fish dying off in a lake and the lake being restocked each year and we were to figure out how many fish were in the lake at the start of the 2nd, 3rd, and 10th years and when it reached zero. Fred had taken a "typical" problem from a textbook and modified it to this. The problems that Fred talked about creating (like this one) have multiple entry points and can be done arithmetically and have multiple representations. There were five he listed but I didn't get them all written before the slide went off the screen. Three of them are Algebraic Formula, Graph, and Table.
The biggest problem that we have as teachers is when we tell students we will help them with the first step or tell them how to figure it out step by step. We need to let the students struggle, for we are not really helping them by telling them what to do. (see more on this in my next post on my 2nd session).
As students are working through the problem and asking questions, things to think about include "How do we handle this? Does it matter?" (at the time it was in reference to decimal values). The most important thing to do is try it and see - encourage students to explore and not to worry about mistakes.
Fred also mentioned that other similar type problems to this one could include compound interest, exponential decay, and half-life of medicines. Once students have completed this type of problem once, you can consider these related problems to see how they can apply their reasoning to similar, but differing situations.
Some other thoughts from what Fred had to say include:
Reasoning and sense making should occur every day. I can see this - it is the main part of math (non-content wise) that can help our students do well beyond schooling.
Reasoning and sense making is NOT a list of topics to be covered.
I have a note about "productive ways of thinking that have become customary" but I have no idea why that is there.
Things that should happen as a part of Reasoning and Sense Making:
**Good Questioning Techniques
**Adequate wait time (and we never give enough of it - we think it's 30 seconds and it's only been 10)
**Resist the urge to tell students everything
How can you get started?
**Recast the material as questions. The opening problem was a typical textbook example.
The other two speakers walked through examples with finding x- and y- intercepts, graphing linear equations, and difference of squares (factoring).
Here's where I am at with this sesssion -
Great topic. I needed to hear this. I need help in how to make it happen in my classroom. I picked up 3 of the Reasoning and Sense Making books from NCTM (25% discount yay!) and they move to my reading list.
But I need to learn how to be less helpful. I know we've talked about this in the math blogosphere and I probably need to search through Dan Meyer's blog to find it. Anyone else have suggestions on how to be less helpful and how to do these types of problems?
Here's the other thing - I still don't get how I am supposed to handle covering the content I am supposed to in my class. When does the teaching go on? Or do the kids figure it out from the problems? How does this all work? I guess that's my biggest issue on "rich problems." I think they're great, but how do I incorporate them into class and still get the content covered that I'm supposed to? Do any of my readers have any insight into this or know of someone who has blogged about it? Any and all help is appreciated.
Basically what reasoning and sense making does is puts the mathematical skills into practice. It fits right in with Race to the Top and the Common Core practices. I think I remember Fred saying that this really fits in with the first one on the list.
We proceeded to work through a problem about fish dying off in a lake and the lake being restocked each year and we were to figure out how many fish were in the lake at the start of the 2nd, 3rd, and 10th years and when it reached zero. Fred had taken a "typical" problem from a textbook and modified it to this. The problems that Fred talked about creating (like this one) have multiple entry points and can be done arithmetically and have multiple representations. There were five he listed but I didn't get them all written before the slide went off the screen. Three of them are Algebraic Formula, Graph, and Table.
The biggest problem that we have as teachers is when we tell students we will help them with the first step or tell them how to figure it out step by step. We need to let the students struggle, for we are not really helping them by telling them what to do. (see more on this in my next post on my 2nd session).
As students are working through the problem and asking questions, things to think about include "How do we handle this? Does it matter?" (at the time it was in reference to decimal values). The most important thing to do is try it and see - encourage students to explore and not to worry about mistakes.
Fred also mentioned that other similar type problems to this one could include compound interest, exponential decay, and half-life of medicines. Once students have completed this type of problem once, you can consider these related problems to see how they can apply their reasoning to similar, but differing situations.
Some other thoughts from what Fred had to say include:
Reasoning and sense making should occur every day. I can see this - it is the main part of math (non-content wise) that can help our students do well beyond schooling.
Reasoning and sense making is NOT a list of topics to be covered.
I have a note about "productive ways of thinking that have become customary" but I have no idea why that is there.
Things that should happen as a part of Reasoning and Sense Making:
**Good Questioning Techniques
**Adequate wait time (and we never give enough of it - we think it's 30 seconds and it's only been 10)
**Resist the urge to tell students everything
How can you get started?
**Recast the material as questions. The opening problem was a typical textbook example.
The other two speakers walked through examples with finding x- and y- intercepts, graphing linear equations, and difference of squares (factoring).
Here's where I am at with this sesssion -
Great topic. I needed to hear this. I need help in how to make it happen in my classroom. I picked up 3 of the Reasoning and Sense Making books from NCTM (25% discount yay!) and they move to my reading list.
But I need to learn how to be less helpful. I know we've talked about this in the math blogosphere and I probably need to search through Dan Meyer's blog to find it. Anyone else have suggestions on how to be less helpful and how to do these types of problems?
Here's the other thing - I still don't get how I am supposed to handle covering the content I am supposed to in my class. When does the teaching go on? Or do the kids figure it out from the problems? How does this all work? I guess that's my biggest issue on "rich problems." I think they're great, but how do I incorporate them into class and still get the content covered that I'm supposed to? Do any of my readers have any insight into this or know of someone who has blogged about it? Any and all help is appreciated.
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