After reading Gallas’ book on Science Talks, I have a lot of information I need to process. The narratives of the discussions her students had and her insights were invaluable. I loved the idea of asking a elementary student why they thought leaves changed, how the moon came to be, and how rice plants began. While reading this, however, I struggled with how I would implement this in my own classroom, especially when teaching mathematics. How would I ask my students to figure out how to solve an inequality using absolute value without knowing absolute value or inequalities? How would my students describe/intuit the meaning of an inequality sign? the straight brackets for absolute value? I’m still struggling with this idea and I hope to learn more about this idea throughout the course.

I really like to idea of bookending a unit with a discussion on how or why one would solve a specific type(s) of problems before giving the algorithms to solve such problems. Such an approach would allow me to see what creative ways they students would use to solve the given problems based on their existing skill set. It reminded me of a lesson about solving systems of equations. I found on NCTM’s website (http://illuminations.nctm.org/Lessons/CandyProblem/CandyProblemAS.pdf). The actual solution to this system of equations cannot be found using any of the algorithms taught in algebra (substitution, graphing, or elimination). I wonder if presenting the students with a novel problem such as the Candy Problem at the beginning of a unit would stimulate and open their minds to new concepts in mathematics.

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I have the same questions regarding how would students figure out certain mathematics symbols and equations, without any prior knowledge. I am wondering how we could incorporate these ‘Science Talks’ into our mathematics classrooms. I feel that we could easily do it with certain topics, like problem solving, where there are a number of correct ways to solve a problem. I am hoping this course will open up some new avenues that I have not yet explored.

Comment by Jeanine Taormina — 01/30/2010 @ 3:04 PM |

Hi Katie,

I am having the same struggles after reading Gallas’ book. As a future mathematics teacher I am trying to figure out how we can incorporate these talks into our classroom of 7th through 12th graders. I feel it can be done with certain units, such as problem solving, where problems are more open-ended with many different ways of arriving at the answer. Other topics though, such as logarithms, would be extremely difficult to conduct a ‘science talk’ when students have no prior experience or knowledge of such terms. I am hoping this course will help me figure out how to accomplish such a feat.

Comment by jrtaormina — 01/30/2010 @ 3:32 PM |

I am also struggling with some of the same ideas. When I read your post and thought about the book end discussions surrounding a unit I was thinking, what would we want our students to talk about? Something that I think is missing in the majority of math classrooms today is the big picture understanding of how concepts in math fit together. When considering how I would incorporate the ideas of science talks in my classroom I am trying not to restrict myself to the specifics structure that Gala used. What about giving students a list of vocabulary words and having them create a project to represent how they are connected to each other and then re-evaluate at the end of the unit what they learned and how their ideas have changed?

Comment by mfm2145 — 02/03/2010 @ 2:04 AM |

Katie, I love the Candy Problem! Funny enough, I actually just starting teaching the unit on solving systems of linear equations today at my student teaching placement, starting with the graphing method. I now plan on using the Candy Problem as a challenge problem once the students have learned all three methods. Hopefully, it will stimulate their minds and get them thinking! I’ll let you know how it goes. Thanks so much for the suggestion!

Comment by hliteracy — 02/03/2010 @ 6:34 AM |

Hi Katie, I struggle with the implementation part as well. Especially, we’re focused on secondary school mathematics. We can’t treat teenagers like first graders, and they won’t respond to us either. Also, math at the high school level is not exactly “fun.” It’s really difficult to come up with interesting questions and examples to engage the students at the teen age. I guess we’ll just have to come up with our own ways to make it work. =)

Comment by amyyuewang — 02/03/2010 @ 8:11 AM |

I think an important thing to consider, when trying to get these math discussions started, is the sentence at the very bottom of the candy problem. “There are multiple approaches to this problem but only one correct solution.” That might be one of the most important ideas to give a student. Just because you and your friend are using two different equations, it doesn’t mean either of you have to be wrong. Be willing to try different ways until you find one that both works and makes sense to you! And as a teacher, encourage them to try different methods and explain themselves.

As far as finding a problem they can discuss, maybe it doesn’t have to be a problem they can answer yet. Bookending the lesson with discussions does sound nice. Maybe that first discussion can be on a bridge question. The idea of transitioning from one unit to another. It would help them see the connections in math (how each idea springs from the previous) and give you a lead in to talking about where ideas like absolute value and logarithms come from. Then, they don’t have to recognize or understand the symbols yet, instead maybe they coud start by understanding why we need/use the symbols. I don’t know if that would be as interesting to 8th graders as ‘why leaves change color’ is to first graders, but it might be a start.

Comment by Courtney — 02/03/2010 @ 5:05 PM |