Subjects Matter: Chapters 10 and 11

            After reading Chapter 10, I am really interested in inquiry projects.  The first example about having students research the population trends of different countries to study exponential functions stuck out to me.  Math is connected to so many different fields and students rarely have the opportunity to see this.  Most of the time students are left wondering when they will ever use the things they learn in math class.  Some of the time they even assume they never will use what they are learning.  Using inquiry projects allows us to teach the mathematics within the context of its real world applications.  The students can learn how exponential functions work while observing population trends, they can practice using ratios and proportions while making different chemical solutions, or they can understand derivatives better by seeing how they are used to describe placement, velocity, and acceleration in two dimensions.  Teaching with inquiry in mind avoids the whole problem of students not understanding why they are learning something. 

            One idea for a curricular inquiry project could be researching how casinos ensure that they are always making money.  This inquiry could involve learning how the different games found in a casino work, calculating the expected values of the games, and coming to a conclusion about what are the most profitable games for a casino to have.  Within this project alone students are working with basic probability, independent and dependent events, expected values, conditional probability, as well as creating inferences from mathematical data.  Just looking at the Common Core standards for Geometry quickly this project checks off HSS-CP.A.1, HSS-CP.A.2, HSS-CP.A.3, HSS-CP.A.4, HSS-CP.A.5, HSS-CP.B.6, HSS-CP.B.7, HSS-CP.B.8, HSS-MD.B.6, and HSS-MD.B.7.  The math inquiry that will probably be very interesting to students since they will learn how many games work (and learn about how much the odds are stacked against them if they were to gamble at a casino) sneakily has them practicing the skills from 10 different Common Core standards.  There is even a potential for making this inquiry into a jigsawing activity as well.  Have the students work in groups choosing different games, then have each group teach the rest of the class about their game and how likely it would be for them to win at it.

Students will learn why casinos entice people to bet on a single number by giving a payout of 35 to 1.  Because there's a greater than 97% chance you are going to lose the money you bet.  Students will also learn why roulette is good game to have in a casino.  Betting red or black gives you almost a 50% chance of winning and when people start winning they want to win more.

            One question I had while reading about these inquiries was: How well does this fit with the principles of UbD?  At the top of page 259, Daniels and Zemelman give the impression that we are coming up with a project first.  We create an inquiry that we think would be a really good idea, and then work from it to see how many different standards we are meeting to justify spending time on the research.  While I definitely like the idea of these inquiries, this seems to be contradictory to UbD.  Shouldn’t we be starting from those standards or a goal from a unit and then working to create a project that fits them? Instead it seems we are fitting the standards to a good idea we had.

            One thought that stood out to me while reading Chapter 11 was how no students seem to like word problems in math class.  I realize that the reason for this is probably because students just do not know how to read them.  As Daniels and Zemelman point out, students “aren’t accustomed to turning the words they read into mental pictures” (pg. 278).  To help this issue, why not give students real pictures to help them form mental pictures?  It’s not that our students are not smart enough to imagine a scenario, it might just be that it’s a scenario that is unlike something they have ever encountered before.  If I had the appropriate technology in my classroom I could have short 5 or 10 second video clips to accompany the word problems to give them context and meaning.  If we are working on a word problem about how far a cannon can fire a cannonball, why not take 10 seconds to watch a cannon fire?  This might be all a student needs to go “Oh!” and then be ready to work on the problem.  At worst it keeps students interested when there are cannons firing off on the screen at the front of the room. 

            Going along with this, I want to make sure to focus on modeling the procedure for solving word problems in my classes.  First we need to talk through the problem out loud.  We gather the pertinent information and decide what is the fluff we can ignore.  We decide what we need to think about, what the problem is asking us to accomplish, and establish a context for the mathematical procedures.  Lastly, we need to make sure our answer matches our expectations.  I have seen this last step being ignored many times already.  While I was teaching ratios and proportions in MATH010, I remember one problem where the students were asked to figure out how many liters of soda they were buying per dollar.  If a student were to set up the proportion upside down they would get an answer of something like .0002 dollars per liter.  The students who did this did not even notice what was wrong.  This is when I realized how important it is to emphasize the relation of the answer to the context of the problem.  Taking the time to think “Does my answer make sense?” cuts down on many mistakes one could make, but unfortunately not many students have been shown to do this.

            Once again what is really most important, though, is creating the supportive relationships that D&Z talk about in Chapter 11.  Students need to feel like it’s ok for them to take risks and that their teacher will be there to help.  More importantly, that the teacher wants to be there to help.  Without this the students are not going to want to put themselves out there, and they are not going to want to risk being wrong in the pursuit of learning something new.