And, amazingly, I will not be finishing this up at the last minute (shocker) as I have already finished my freebie and my post days ago. I made a math game for working on your quick ten facts- so be sure to hit me up Sunday for it! And then there's going to be tons of other freebies too from the other bloggers. Come see EVERYBODY!
And on to math.
Hey- I finished Chapter Four of Laney Sammon's outstanding book: Building Mathematical Comprehension. Chapter Four is about the reading comprehension strategy Questioning, and how it applies to math. Lots of meaty goodness here- especially when we start right off the bat with this quote on page 115, "one of the most effective ways one learns is through questioning." And then you get just a few paragraphs further and see how curiosity in math has dried up by middle school because as teachers, we've created an environment in math where asking questions relates to a lack of knowledge as opposed to interest. We've focused so much on there being A CORRECT answer that we've squelched the possibilities of exploration. So here's another killer quote on page 116, "When the teacher is solely responsible for asking questions, students become disenfranchised. Students need to know that their questions matter and are valued."
So the root of question is quest. A quest! An adventure! I had NEVER thought of it this way. Really gets me thinking about problem solving and engineering in the classroom and how all these years its just been formulas and worksheets. But you see, I was an English major, and this was one of the things I felt like I liked about math- the lack of subjectivity. I LOVED having AN ANSWER as opposed to a million different viewpoints. And so I'm reading this chapter thinking to myself- well shi-oooooot. I've been a curiosity killer, dang it. Let's add that on to the long list of things to feel guilty about.
Luckily though- the chapter offers some solutions. One great link (oooo-connection) I can make to help me out is that I had some training this year by the great Jan Richardson herself- who wrote The Next Step in Guided Reading. She has a technique of teaching questioning in reading with green, yellow, and red questions in relation to how easily/difficult it is to find the answer in the text. Laney has a similar outline to questioning with what she calls Right There, Think and Search, and On My Own questions in relation to math. Already knowing this similar strategy really helped me put this part of the chapter in perspective. And also, clued me in to when I get to teaching it to my students- I will probably combine the two phrasings to have Jan's as the "title" of the type of question, and Laney's as the explanation for it means. That way I'm teaching it with the same terminology in both venues.
Laney goes further to add in the difference between thick and thin questions which is also important to teach children as they construct meaning. I really enjoyed the part of the chapter where she outlined a strategy lesson where she taught the kids how to generate questions about a problem and then go back and determine if the question they asked would actually help them come up with an answer. So important to model and provide this foundation for the kids. You know as a teacher how often kids just ask odd-ball questions out of seemingly nowhere, and don't seem to be able to determine for themselves whether it was applicable to the situation. At least this way, you can still validate them for their questioning, but also teach them how to evaluate that question that they asked.
Again, I also like how Laney is using ideas from Comprehension Connections by Ann McGregor which is another book I'm familiar with. The same thinking stems you create in reading class, are the same stems you can use in math class. I don't have to come up with something new! I can use the same thing all across my day and really provide valuable links and connections for the kids so they can experience learning as a whole, rather than disjointed subject matters. Maybe this means there could be an end to "which subject do you like best?". If they are all infused with the same backbone- do they need to make a choice? Aren't they now offered the possibility of loving them all? I don't know. I realize that I just went off into a little philosophical corner of my brain there. I'm getting awestruck by how much of this profession I just DON'T KNOW yet.
One other part of this chapter that I really liked was the Questioning math stretch- which again, I can connect to some prior knowledge from her first book, Guided Math which discussed math stretches every morning as part of the small group teaching model. In this stretch, the idea is to present kids with a problem solving scenario without a question- and then ask them what the question should have been. Very Jeopardy. I'll take "richer thinking experiences" for $200, Alex. I've seen something similar to this, but not exactly the same. Here are three pins I've had on my math boards for a while now and was seriously considering doing in the classroom this year. And I'm not saying that I still won't- but look at these three and ask yourself two questions:
1) What do they have in common?
2) Is this rich, higher level thinking?
Completely no disrespect to these pins- I STILL like them. I STILL will use this to some degree in my room, I believe. Like a warm up, because there is validity in being able to come up with equations - but this idea can be taken farther- and it should.
What I saw they had in common was that the "answers" were equations. And where I can see the argument that this is higher level thinking in terms of having the children think in reverse- it's not really, rich, is it? there is still only ONE way the kids are determining their "answer" - an equation. I feel like when I look at these now, after reading the chapter- I'm still squashing curiosity if I present this model. Laney's idea for the questioning math stretch is to present the problem this way-
"Mrs. Hall's fifth-grade class is planning a party for their first-grade reading buddies. They plan to serve pizza and punch at the party." -pg.139
Think about that! what happens when you ask kids to think of the question on that one? Are you going to get an equation? Heck no! And that's why I like it. The equation is not the first stop. Or even the last. The kids really have to think about what they would need to know to CREATE a math problem.
Of course, this line of thinking leads me back to an earlier revelation I made during my reading and e-courses this summer. Teaching this way, is going to be A LOT of work. Like, I will never be able to "wing-it" through another day. It really shows me how lazy I've been in my career to this point. and having said that- I can think of many times where I felt I worked my butt off. So, am I brave enough? That's the real question...
There are other folks who have written blog posts on this chapter through a book study hosted by Primary Inspired- go check those out!