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.

Subjects Matter Chapters 8 and 9

        My favorite part of Chapter 8 ended up being about how we can use web tools to foster conversations between ourselves and the students, and between the students themselves.  In a classroom where all the students have access to the internet at home, there are many ways I could put this to good use.  The book has mentioned the Edmodo website several times now, and I really like the idea behind it.  Instead of hastily assigning homework at the end of class, the homework is directly sent to the students.  This eliminates the problem of “not knowing there was homework” when the expectation of checking the site every night has been established.  It also gives me a great tool to help students be prepared for the next day and even give helpful reminders or convey something I forgot to mention in class.  I also like the idea of having a blog for the class.  I picture it in my head working somewhat like Ask Dr. Math, only with the option of having many different sources of responses. 

http://mathforum.org/dr.math/

The website that everyone has probably come across at some point or another after getting to the point of typing out the entire math question into the search bar.

Having a designated spot where students can ask questions from home should quell the desire to give up when encountering a problem that they just can't work out.  On our blog a student can ask about any problems they are stuck on.  Other students can go on and they might notice a few of them have the same issue.  From here they can work together and figure it out, or I now have a convenient spot to answer everyone’s question at once.  This is a lot easier for me since the alternative would be replying to several individual emails.  I also think it is beneficial for the students to see one another having trouble so they do not feel like they are the only one having a problem.  Some steps would definitely have to be put in place to avoid this becoming a crutch for students, but I think something along these lines could be a great addition to a math class.

            After reading both chapters I began to think about how I can adapt a book club to a math classroom.  I do not see myself having a true free reading book club as part of my math class since I would like any free time to be focused towards improving math literacy specifically or practicing new and interesting math skills.  One idea I came up with is a take on Dr. Brell’s “Catching the News”.  Once a week, students could bring in stories they find about math, engineering, technology, or anything that involves calculations and computations in some way to share with the rest of the class.  This could be an easy way to help students gain some points or extra credit.  Also, what most likely starts as something the students do to get some points could turn into a student discovering something they are really interested in.  Maybe they read an article about a new software that has been developed and they find it really cool and start reading about how programming works.  I think it would be awesome if I was able to create an opportunity where a student finds a new interest or even a potential career choice. 

A second idea I had would be to have a weekly math club.  Combining a few different ideas from the chapter into one activity, this could be allow for a student assessment of my teaching, a student assessment of themselves, students practicing audience accountability, and a low risk grading opportunity.  Once a week, students could gather in groups of four to talk about the current topics we are discussing.  They would be given organizers where they write down one thing that they feel they learned, one thing they have a question about, and one thing they would like to know about next.  These could be filled out as a group or individually.  If everyone has a different question I would not want to limit the group to only asking one.  In terms of me assessing the students, if every student hands in a paper that is filled out they get full credit. 

One last idea I had that would practice independent content area reading and foster student choice would be to have a long term project relating to the history of math.  Students would choose the time period they are most interested in and work in groups to create a presentation about prominent mathematicians and what types of mathematics were developed during at that time. 

Pythagoras.  This is the guy everyone thinks of when you need to find the sides of a right triangle.  The theorem may be named after him, but did you know that the Babylonians who lived 1000 years before him already knew how the sides of a right triangle were related? How about that Pythagoras was a vegetarian and he required his followers to be vegetarians as well?  Or even that the students of his school also had rules like "Do not look in a mirror beside a light"?  All of this could be genuinely interesting to math students and for some reason is never covered in high school math classes!

Before this project starts, I would give a brief overview on several different periods to help students make a clear and informed choice.  Groups would meet periodically to talk about what they have learned, practice doing math the way the people of their time period did, and decide what they want to research next.  I have a lot of responsibility here to help groups stay on task, guide them in their research, and make sure everyone is working to benefit the group.  I think it would be worth it though, and many of the students might find what they learn interesting and engaging.

            Once again, two chapters about things I never imagined even thinking about while designing my future math classroom have given me plenty of great ideas I can try.

Subjects Matter: Chapters 6 and 7. Math Team

           Chapters 6 and 7 of Subjects Matter reinforced the need for reading and comprehension strategies and then began to establish how having a community of learners can help our classrooms.  Some of the advice that stuck with me regarded how we, as the teachers, need to filter our textbooks.  There is no need for the students to read every word in a textbook and this is even advised against.  Reading every word would not engage any student, never mind help to foster a love for the content.  This is why it is very important that we know our textbooks inside and out.  Knowing exactly what is inside helps us to decide exactly what is most important for our classrooms.  This might not be the same for everyone, but with only 180 days at our disposal, its important to have an opinion on what are the central concepts of the course. 

Another great piece of advice is to know exactly what are on those “big tests”.  For now anyway, it is clear that what is tested by the standardized tests needs to come first.  We still have room to explore and supplement, and we absolutely should, but leaving out something that will be tested on in exchange for a fun activity could be disastrous.  One of our responsibilities in the current educational climate is to become masters of the standardized assessments.  This idea is actually very in line with UbD and backwards design.  If our students are going to be taking these tests, we should start by examining the assessment, and then craft our lessons based on what we know is on the test.  Planning this way allows for teachers to prepare students for the standardized tests while hopefully making an effort to craft interesting and engaging learning experiences.  Last summer I took a course on teaching Calculus with Dr. Humphreys, and she also stressed the importance of becoming an expert on the test we are preparing our students for.  The AP tests are very different from PARCC, but the lesson is still the same.  If I am not absolutely sure of what is going to be on the big test at the end of the year, how can I make sure my students are ready for it?

            I also really appreciated the shoutout to how math textbooks are very different from the rest in Chapter 6.  As I have been doing all the readings this semester, I keep thinking “But my math books are going to be so different, does this really apply? Or how can I change this so it does apply?” Reading this section just makes it even clearer that I need to really focus on these comprehension strategies to make the math textbook digestible for students.  Part of why students have such a hard time with them is definitely because how different they are from the rest of the textbooks!  Reading on their own, if a student does not understand a sentence somewhere along the line in their history book, they will probably still be ok.  They can still take away the main ideas from understanding everything else in the reading.  In math however, not understanding one sentence might handicap a student for that whole section, that whole unit, or depending on the sentence, the whole course.  This is a very serious matter and I need to do something that I did not expect I would be doing as a math teacher before this semester.  I need to arm myself with a full arsenal of reading and comprehension strategies and employ them every day.

            While reading Chapter 7, I was immediately reminded of an article I read last semester while “Catching the News” in Dr. Brell’s class.  “Teaching in the Shadow of the Ferguson Shooting” was written by Inda Schaenen and appeared on edweek.org last September 4^th.  In the article, Mrs. Schaenen explores all the difficulties she will face teaching her 8^th grade language arts class this year.  She knows that the children do not feel safe in their community.  Many of the students deal with the events in seemingly odd ways, even going so far as re-enacting Michael Brown’s shooting in the school.  What I really took away from reading this was that these children are not going to be able to learn until they feel safe again.  They have way too much on their minds and way too much to be worried about to focus on their notebooks, worksheets, and textbooks.  None of that matters to them when they are afraid. 

In Maslow's Hierarchy of Needs, you need each bottom layer to have the layer on top.  Without food and water, a person can not feel security and so on.  Bringing this ideology into the classroom, we see that "achieving one's full potential" is at the very top.  Before students can learn, they need to have the basic needs, feel safe at home and at school, and feel like they belong.  As teachers, we need to try our very best to making sure that all our students feel safe and included.  If a student feels like he or she really belongs in their math class then they will start to succeed.

            I really believe that a classroom community needs to come first and then learning comes second.  And when learning comes second, it is more efficient and more powerful.  Daniels and Zemelman back up this point saying “In schools where teachers explicitly taught the social skills of small-group interaction, the students gained an average of 11 percent on both their course grades and on high-stakes standardized tests given in their state.” (Pg. 203-204)  When students feel safe, then they can focus on all the other things.  When students aren’t worried about being made fun of, aren’t embarrassed to make a mistake, aren’t thinking about whether the bully will stop them in the hall today, that is when they can get excited about learning something new.  Something that I want to do with my classes and something that I think about a lot is turning my classrooms into teams.  I am still not even close to having a fully realized idea, but I know this is something that I will develop and I will put into practice.  I never want to really have a “class”.  “Class” can have a tendency to invoke an image of desks in rows, children working silently, and a teacher in command.  I want to have teams where the players learn together and understand the benefits of helping one another and working for a greater good.  I want to be the coach of this team.  Someone who knows the game of math and can help them execute all the strategies.  I hope that doing this will bring my students and myself closer together and create a space where cooperative learning can take place.