Subjects Matter: Chapter 12

           Even though throughout reading this textbook I already trusted Daniels and Zemelman because all of their recommendations and strategies really made sense to me, it was very interesting to see all the studies and research that went into the making of Subjects Matter.  There were a few points that stood out to me in this last chapter. 

The first was there reassertion that “students should read a wide range of materials and genres of text in all classes” (pg. 294).  Over the course of the semester this has become a point that I really agree with.  As adults we come across a huge variety of texts.  We read doctor’s reports, tax forms, legal documents, blogs, e-mails, and our books for pleasure.  If as teachers we only take the time to teach our students how to read Shakespearean plays or Poe’s poems, how are we preparing our students for life after high school?  That’s not to say reading those things aren’t important, but there is so much more out there our students should be ready to encounter.  And the fact that they feel confident when they do encounter these texts is what lets us know that we did a good job during the four years we had with them.
            The second was that “students should read plenty of materials written at a comfortable recreational level, and gradually move up toward more challenging text as the necessary supports are in place” (pg. 298).  At least from my own high school experience, I feel that this is something that gets forgotten much of the time.  There is this big focus on challenging students to read at or above grade level, to have them analyze and pick apart texts, and draw new conclusions from what they read.  We forget that students can’t analyze and synthesize if what they are reading does not make sense to them.  Becoming a better reader is not like becoming a better athlete.  If you want to train to be a better athlete then you play against people who are better than you.  Even if you lose it doesn’t matter because the fact that you were challenged helps you to be faster, stronger, and make better decisions.  If a student “loses” when he’s reading then he does not take away any positive lessons.  He starts to feel that he is not a good reader, that he can’t do this, and that he’s falling behind.  These feelings don’t motivate students, but give them all the reasons they need to give up.  Becoming a better reader happens when the student is successful.  If a 9^th grade class is learning how to find the themes in a text it should not be taboo to do it while reading something that might be at a 6^th grade level.  We should only want to be teaching one new skill at a time anyway.  The lesson is about themes, not about reading complicated words or phrases.  We will get to finding themes at a 9^th grade reading level eventually, but starting slow builds confidence and still helps the student practice reading even though it’s “below their level”. 

The third point that stood out to me was how we can teach students to read by having “teachers make their own reading habits and processes visible by regularly reading aloud and by explaining and modeling their thinking about content-area texts” (pg. 299).  Dr. Abrahamsen (RIC math department) often reminds his students “Math is best read with a cup of coffee and a pad of paper”.  This could not be truer.  When you are reading a math text you need to follow along, do out the examples, and check your understanding at each step. 

Search on google for a mathematician working and there is not a single picture of a person statically reading.  The only way to learn math is by reading and doing.  Students can't just be expected to know this is the way though.  It's the job of the teacher to model this and give them a space to practice this.

Reading one page of a math book should not take the same amount of time as reading one page of a storybook.  This is something I really want to make sure my classes understand.  It may take more time initially, but the gains you make from practicing proper math reading strategies are enormous.  You gain a clearer picture of the material and if you work problems out for your self you will remember the process and the results for much longer. 

I want to set myself a goal for my first year teaching.  I don’t want to fall back on what I'm comfortable with.  I don’t want to settle for just doing math at the board and having students copy the routines and just learn the steps.  I want to bring literacy into my classroom and I want to bring reading into math.  Students in my class will be able to answer “Why?” at every step along the way.  They will know how what they are doing on Monday connects to what they did last Friday, what they did last month, and what they did three years ago.  They will know how it connects to what they will do on Friday and what they will do at work or in college.  I’m writing this here to set the challenge, and now I have to meet my goal because now a bunch of other great future teachers know what should be going on in my classroom.

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.