Wednesday, June 26, 2013

Book Blogging Buddies--Chapter 3!


It's my turn!

For those of you following along with our collaborative book study, it's my turn to share an overview of a chapter.  Chapter 3 provides a foundation for "getting started" strategies.  As you know, sometimes getting started with anything is the hardest part!  Take this photo for example . . .


Please don't judge.  I have other strengths. 



Where do I even get started on this little project? This is a combination of the stuff that has piled up on my counter and one drawer for the last  . . . um . . .. school year.  It's so overwhelming to tackle that I have simply shut down and avoided it.  I think some of our students feel this way when they see a math problem!  There is so much there and no clear direction.  So  . . . I'm going to try to tackle THIS problem using the steps in this chapter.  Bear with me!

The entire premise of chapter 3 is a set of 4 "strategies" to use when addressing a problem.  Gojak stresses that these can work for tacking routine and novel problems and can be used at any point when you reach a roadblock.  Here they are:

  1. Restate the problem in your own words.
  2. Identify wanted, given, and needed information
  3. Identify a subgoal
  4. Select appropriate notation
OK--here goes.  For the first strategy, we need to "restate the problem".  In a math context, this might involve the student reading and reread the problem to get familiar and comfortable with it.  I love that she talks about visualizing the objects and activities in the problem.  I go in waves where I work on this with students, but I am going to do more and more of it next year.  

In my non-math example, I think it's pretty easy to restate the problem.  I won't put words in your mouth--go ahead.  I can take it. 
{Insert descriptive language here}

Moving on . . .

The next strategy asks students to "identify wanted, given, and needed information".  The book points out that this is the time when students need to decide if they need more information from another source, whether there is insufficient evidence to solve it, or if they need to do a step before they can actually get the final answer.  The author even suggests that we have students get in the habit of recording wanted, needed, and given information as they solve.

So, moving back to MY problem.  I think it's clear that in order to solve this problem I need to find out what I have, what I need to keep, and then find places for the rest.  This may mean that I need to create places (ex. folders) for some of it.  It also means I need to make some hard decisions about what is really important!  In order to solve it, I need to be clear about what I need to keep and what I can let go.  For example:

Now on to strategy #3--"Identify a subgoal". Gojak explains that this is closely connected to the last strategy. Students need to be able to recognize if certain actions need to be done before a solution can be reached.  These multiple step problems can be particularly tricky for some students!  She stresses that students need to show their work at each step so they can share their thinking with others.  I would add that it makes it MUCH easier to troubleshoot when the steps are clearly laid out!  

My subgoal?  Sorting my pile into categories.



Finally, we need students to be able to "select appropriate notation".  This is a huge part of the "precision" component of the Standards for Mathematical Practice, so we need to get even our littlest mathematicians in the habit of this!  Whether we use numbers, pictures, symbols, charts, or other--students must be deliberate about how they represent their work.  The next chapters of this text will dive into this in more detail.

As for my problem?  I am going to say that MY appropriate notation involves some hanging folders and a recycling bin!  

So . . . let's hear your thoughts!  The author has started us off with the following three questions:

1.  How did these problem-solving strategies help you to solve the provided problems in this chapter?  (I really DO recommend you actually try them with these problems!)

2.  How will these strategies help students with comprehending the problem they are trying to solve?

3.  What steps can you take to teach your students how to use these strategies when solving problems?

And if you finish all those . . . feel free to come on over and help me with my laundry room!




8 comments:

  1. A teacher after my own heart! No judging from me. :)

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    1. HEHE...I knew there were a few more of us out there! :)

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  2. Only 1 comment so far?! I was waiting till the end of the day so I could read everyone else's comments, and then make my own! OK, I guess I'll be the first one to start.

    I liked this chapter. Short and sweet (just like I like my math problems!). Unfortunately, many math problems aren't that "short," and definitely not "sweet" so what do we do when we come across these problems? We need steps, just like the ones provided to us in Chapter 3.

    I love that Gojak has given us strategies to break down word problems. In fact, I feel like creating a poster that states these strategies as a visual reminder to me and my MS students.

    I kept reading the phrase "get students in the habit..." or "create the habit of mind...". These strategies must become HABIT! That means we need to practice, practice, practice these strategies until they become second nature. But are math word problems the only way to teach these skills! Absolutely not! Just like Meg's example of the counter clutter (which I believe is on every teacher's kitchen counter at home) we can take real-life non-math examples and teach these strategies!

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    1. I agree Mandy!!! The problems were difficult. Yes, I looked in the back for answers (haha). I now understand that this way of thinking in the Launch stage will have to be developed s-l-o-w-l-y and painlessly on the students. I heard the students groaning because I was groaning. At first, my mind needed to build stamina as I focused. The desire to skip the restatement was great in me. So too, shall it be with the students. I would immediately try to go to formula notation but I yielded better results with making a chart. I did enjoy the identify, wanted, given information stage. This is the stage that had an element of puzzle fun.

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  3. I totally agree about the anchor chart--have it in my notes to make. As the problems get more complex, we have to really coach our students on not just the MATH, but on the perseverance and "behavioral" strategies to allow them to struggle, keep working, and know how to tackle it step by step. Thanks for your comments!

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  4. Most of my comments are in reply to Mandy's response, her comments resonated in me. Another strange thing occurred as I tried to discipline myself to adhere to the process. I would begin skipping around as if I was brainstorming and trying to adhere by memory with no notes in front of me. My problem solving notes began weak but I ended stronger. I'm going to have to be accepting of this from my students as well. Going through it myself helped me to understand the strange pieces of work that I will encounter at the beginning.

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  5. I also agree about making an anchor chart to remind the students about the strategies. I also learned an important lesson in a workshop that I attended this week. As teachers we do not always give our students time to get started on their own. If they complain about not getting it or seem to struggle, then we want to jump in and help them. Sometimes the best strategy is to back off and let them work it out on their own or in a group.

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  6. First of all, my room resembles yours. I have a 16 year old going to camp next week and I plan on going to school to tackle those piles I procrastinated on.
    This chapter is what I have been working on with my students. Then I get pressured for time and stop the process. This reminds me of how important this is. Anchor charts are an amazing tool that I use in everything I do. I have 2 rotations and go through them with each group and then combine them so each class is represented (we had some silly word problems for 2x2 multiplication)

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