I’m into the second month of knowing my mom has terminal cancer. While I’ve had time to ponder the idea, her pain is increasing, so I’m constantly coping with something new and it is not getting easier. I read that when one is truly sad, helping others is a good way to change that feeling. I still have my energy (largely because I quit my job and my classes to take care of my mom) so I’m headed to the schools of Phoenix. I feel safe in the world of academia, but it is in the schools where I can make a difference that I can see today in the life of a new teacher. I need to see my work helping today, not years down the road.
Thankfully, I found a new teacher wise enough to accept help and I can only hope that I can be for her what she needs today. I have this instinct to tell her everything about everything, and I know that it doesn’t help as a new teacher. New teachers are constantly getting advice that sounds great but they just can’t make happen in practice because their brains are not yet wrapped around all the day to day details of being a great teacher. I recall getting advice about how to improve lessons that just made me feel guilty because I didn’t have the energy to implement it.
So my goal for today, is to leave some of my more than a decade of experience teaching and tutoring math at the door and commit to doing whatever I can to make this new Corps Members life better today.
I read Kool-Aid’s entire first year blog yesterday and I came away feeling that TFA both did her wonders and hurt her deeply. They helped her define and express a huge passion for changing her kids lives and putting her everything into teacher. They also led her to believe that great success was possible in her classroom when in fact, that is not actually the case for a first year high school math teacher. (If anyone has evidence to the contrary let me know-even the secondary teacher who won Sue Leyhmenn had assessments all at low levels of blooms with mainly memorize and recall items.) I absolutely believe the kids we encounter have what it takes to think logically, to solve complex problems, to improve their understandings of mathematics and to graduate from college. I also have evidence(from research papers, from our blogs, from the classroom) that some of the students we serve in high school are struggling with 3rd and 4th grade concepts. I saw a blog entry on Kool-aid with someone who was struggling to count by fives-this is something my six year old niece can do.
So as a high school math teacher, the holy grail of 1.5 years growth could literally mean getting some 10th graders to a 4th or 5th grade math level. I can’t even imagine telling a MLTD that your big goal for your 10th graders is to get them to a 5th grade level. However, I do think this goal is both ambitious and feasible, even thought I would NEVER message it to my students, the parents or the principal. Even though I believe in students’ endless potential and have seen seven year olds say and think amazing things mathematically, I also believe that we can only build knowledge on what we know and that to meaningfully understand high school math requires meaningfully understanding K-8 math. I’m not saying that plenty of Corps Members(myself included) don’t successfully teach high school algorithms that do have some meaning for the kids. But I do think that to form a truly coherent, connected picture of secondary mathematics students must deeply understand counting, place value, fractions, decimals, and the meaning of division, just to name a few ideas.
In Kool-aid’s blog I saw a number of examples of students who did not have a meaning for subtraction or division. For example Kool-aid told one student that there was 25 feet between them. Then she said to imagine walking 5 feet closer and asked how much distance would be between them now. The student was stuck until Leslie said imagine 25 takeaway 5. To the student takeaway corresponded to the subtraction key on her calculator and she used it to figure out 20. To me, this student does not have a quantitative image of subtraction. Geometry is dependent on representing sums and differences in lengths with addition and subtraction. I’m not sure how to build up to advanced knowledge without an image of what it means to subtract a length.
But I don’t feel like I can just TELL a new teacher all of this. I absolutely, certainly, don’t want them to think that their kids are dumb. It’s not that they are dumb, but they may be damaged by the system they grew up in. Damaged in the sense that their meanings for basic operations do not support future learning.
For example, I know kids who do not have strong meanings for basic math fact can solve the difficult mutilated chessboard problem I first saw in college.
Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares?
Leslie found that her students who were struggling for weeks to find the volumes of geometrical figures were also totally excited and productive trying to solve the World’s Hardest Geometry problem.
So at the same time that I believe that a reasonable big goal may be getting a 10th grader to 5th grade math level, I also believe that hard problems I found in college may be within their reach. Their thinking isn’t broken just because they have not learned something. Just because I don’t know Japanese doesn’t mean that I couldn’t learn it or that I’m dumb-I just haven’t had the chance.
It’s important to note that I don’t think the past teachers are necessarily to blame-I think that most teachers try (TFA or not) but that most math teachers are not supported with quality Professional development or curriculum. I think that almost all teachers want the very best for their children. However, some have experienced failure so many times when trying to catch kids up 6 or 7 years to meet the demands of what they are asked to teach that their enthusiasm is strongly damped by an unpleasant dose of failure.
So I’m off to help a new math teacher and I hope I can leave at the door all my big questions about just how to balance a sense of possible with reality, and push yourself as hard as you can to teach well without pushing yourself off the edge. I don’t want this teacher to end up in the dark place Kool-aid and I found ourselves in our first semester of teaching math.