Solving Equations = Battlefield

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So, in tutoring the other day, I was helping my 9th grade student in solving equations.  He was having trouble seeing that he needed to combine like-terms before flipping things across the equal sign.  I told him that he needs to “draw his boundary line” down from the equal sign, so he can see both sides of the equal sign.  Then, I used the analogy of having a water balloon fight across the creek (boundary line) and that you need to get all of the “teammates” (like terms) onto the correct side of the boundary line (equal sign). He seemed to understand it better after that!

 

draft started in October 2013, finished August 2022.

Thoughts on “Leading for Learning”

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The following is my take on an article that was in the Fall 2012 issue of American Educator, page 24-33.

The authors started out researching successful schools in high-risk areas to see why they were effective.  They discovered the principals to these schools were “It Can Be Done” leaders, and continued to break down what made those people so successful.  The thing that really stuck out to me (and this is really just common sense) was that the best principals were first teachers, and were teachers for the majority of their career.  This allowed them to see what it was like on the other side of the desk, and they did it long enough that they remembered what it was like to teach once they “got to the top”, so to speak.

The other major thing that stuck out to me was that these successful principals never stopped thinking of themselves as teachers – they were just changing their target audience and thus became a teacher of teachers.

It made me think of my previous schools, and my previous colleagues, and wondering what their reaction of the article would be.  I imagined who would read it and say, “Ugh! This is just more of that Thoughtful Ed, waste of my time, crap!”  I also thought of who would read it and immediately take the cop-out response of, “Well, I’d love for our administration to do things like this, but they won’t so, whatever.”  I feel like there are some times we act just like our students – defeatist, tired, comfortable.  We complain when our students don’t know basic things, yet throw our hands up and play the blame-game saying “Well, they just can’t be taught.”  Bull.  That’s when I turn into one of those cop-out people and say “I wish our administrators were one of these It Can Be Done leaders, but…”

I need to learn to stand up to my colleagues and call them out on some of this stuff.  However, I hate feeling patronized when they retort with “Oh, you haven’t been teaching for 15, 20, 30 years…you’ll see.”  I hope I never become complacent in my teaching.  I always want to be reevalutating my methods and asking myself if I’m being an effective teacher for each particular classroom.  No one is perfect, and we can all learn from each other, no matter how many years of experience we have.

 

Multiple choice questions are deceptively difficult.

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I am convinced that if given the choice, people will choose to do a multiple choice question over a fill-in-the-blank/short answer question which asks the same thing.  Reasoning could be explained that they have a better chance of getting the answer correct by having the correct answer in front of them (most of which having a 1 in 4 chance of picking the correct answer).  However, people tend to forget that many teachers (especially math) can give partial credit if work is shown  with a short answer question, particularly if some conceptual knowledge is displayed.  This cannot be done with multiple choice questions.

Many standardized tests can use this theory to their advantage, and can in turn become tricky with their multiple choice options.  In my opinion, the authors of the Integrated Algebra Regents exam are most comparable to the New England Patriots – they seek out your weaknesses and then drill them all day long.  The authors of the Integrated Algebra Regents know what students have difficulty with, and what mistakes are commonly made.  They will work out the problem using these common mistakes and make that an answer choice, causing the majority of students that make that common mistake to pick the wrong answer.  A good student will not make those mistakes in the first place.   A great student will recognize these tricks and use the process of elimination to help them ensure they have the correct answer, or at least a better chance of getting the right answer.

The Regents exams (math, at least) are complex exams.  They not only focus on the content being tested, but on how well a student performs on tests.  With the complexity of these exams, and the stress of performance effecting teacher evaluations, how can we blame teachers for teaching to the test?  Yes, ideally, if content is focused on, the students should be able to demonstrate their mastery by content knowledge alone.  However, if no instruction or preparation is given to show the students the nature of these tests beforehand, even the most competent student could fall into the trap of making common mistakes and choosing the wrong answer.

 

How I Would Fix Math Education

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I am in a unique position of being highly passionate about math, and loving to work with kids of all ages.  Middle school is my favorite level, though most people upon hearing that exclaim “WHY??!”  In my unique position, I’ve seen math fads come and go.  I’ve seen politicians get passionate about math education (mostly because we’re way behind the curve compared to the rest of the world).  I’ve seen administrative-types develop curriculum that will “cure us” of our math problems – people who haven’t been in the classroom since before I was born.  I’ve been in every level of a class that you can imagine (primary, elementary, middle high, high school, college) as both a student and an instructor.  Here is my professional opinion: Our students are lacking the foundational base needed for higher-level mathematics.

Now, I know what you’re thinking – “the drill-and-kill method didn’t work on me, why would it work on my students?”  My theory is that we haven’t really gotten away from the drill-and-kill method, and it’s killing us.  We just changed the way “drill-and-kill” looks.  Ask yourself – How do I add fractions? (I know, the “f”-word!)  Most of you would say (I hope) that you need to find a common denominator, add the numerators, and you’re done.  But, do you know why we do that?  I bet if you thought about it, you’d be able to figure out the reasoning behind our procedure.  How about 2-digit multiplication – why do we need a place-holder?  Because that’s how we were taught to do it, and that’s just the way it is? (Are you starting to see my point?)

Many of the teachers that we have in elementary school – while competent teachers – are not trained enough in math education, and therefore end up teaching things the way they were taught, perpetuating the “drill-and-kill” method.  Many suffered through elementary math methods class in college (I know, I tutored many of them) and went on to teach the way they were taught regardless.  I don’t blame them – they have 3 or 4 other subjects to worry about as well, not to mention the character development that is important to incorporate into their learning.  They don’t have the time to spend on developing math comprehension – not when English (reading mostly) takes up half the instruction time, and the almighty New York State Tests must be given in May, which teachers are more worried about this year than ever before.

Another wrench thrown into the mathematics education problem machine is the curriculum, that is fueled by the standards.  Elementary students now need to start trying to understand algebra concepts, as well as probability and geometry.  It’s hard enough to explain algebra to a 7th grader, let alone a 4th grader that barely has his multiplication tables memorized.  If we instead focused on more basic comprehension of arithmetic in the lower grades, we would have the foundation the secondary teachers need to be more effective with their specific subject areas.

My proposal is this: since we cannot readily change the Common Core State Standards – that EVERYONE is using as a model – we should better train our teachers in the math concepts they are required to teach.  There is no such thing as “math magic” and those that believe there is are just kidding themselves.  If we can communicate better between elementary and secondary staff, the secondary expectations can be better realized by the elementary teachers.  In the same way, the secondary teachers need to realize that the elementary teachers are being pulled in many directions already.  While they may strive their hardest to get students to the level of expectation of the secondary teachers, in some cases something needs to be sacrificed to maintain sanity.  If we have a better understanding of each other, we can be a more united front in the front-lines of education.

Rapid Review

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This is a review strategy that I used with my one-on-one student today.  She has a math test today, so I went to the chapter review section in her book.  There were about 30 questions in the section, so I got out my 20-sided die, as well as 2 whiteboards and markers.  We took turns rolling the die, and whatever number came up, that was the problem we worked on.  We worked on the same problem independently, and then checked our answers after we were finished.  If our answers didn’t match up, we knew something was wrong and needed to go back and check our work.

This would also work great with partners in a regular-sized class, with the teacher moving around to monitor, making sure that both partners are putting in the effort and checking for discrepancies.

We started this with the last 10 minutes of the period, so obviously couldn’t get through all 30 problems, but it gave her enough of a random review that we got one type of each kind of problem done, and she is better prepared for her test this afternoon.  It was a nice, quick review, that takes little set-up time and allows you to jump right into learning.

The Elephant in the Room is sitting on my chest…

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This morning, we had our monthly faculty meeting.  We discussed important dates and events that will happen in the final push of the year – 37 instructional days left!  I can’t believe it.

Then the tone got heavy.  We talked about all the state mandated changes to happen before September.  Let me preface this by saying any one of these changes is a major undertaking in itself, and each seems (in its ideology) like a great thing to be doing, but we have 6.  Yup, six.  And about 2 months to learn how to do each one correctly and start implementing them.  And, oh yeah, teach your content as well.  And, each of these changes comes with their own set of terminology and acronyms that we must now understand upon hearing.  As each one of these six new state mandates went on the board, my head spun a bit more, and I sunk lower in my chair, and I started thinking just how good North Carolina was looking right about now…

1. Benchmark Testing – These tests will take place every 6 weeks.  They are not the typical tests that you already give to your students (we wouldn’t want to make this easy on you).  These tests, ideally, will help teachers to know what needs to be retaught and what students really aren’t getting the content.  Again, this is somehow different from what teachers already do…don’t ask me how.

2. Student Learning Objectives (SLO’s) – Many mixed messages about what these actually are and their purpose.  I thought I understood it, and then they changed the wording again.  It seemed to me that they were a way for non-regents teachers to be evaluated on student performance as part of the APPR.  However, now Regents teachers are also included in this in some way, which is the part that doesn’t make sense to me.  Regents teachers will now be evaluated on how their students perform on the Regents, and meeting these objectives (that they also have to create, by the way).

3. Data Driven Instruction (DDI) – Theoretically, this makes perfect sense.  You change what you are teaching based on the percentage of students not understanding material.  Where it starts not making sense is how this is different from Benchmark Testing (which I still can’t figure out how that’s different from what we do already…more paperwork maybe?)

4. Common Core State Standards (CCSS) – This basically states that all content areas need to include literacy.  Each teacher must create 2 units (1 each semester) in which literacy is embedded and an integral part of their unit, no matter the content area.  Again, don’t ask me how this is different from what we already do…probably paperwork again.

5. Dignity for All Students Act (DASA) – An important thing to happen; unfortunately it may be eclipsed by the 4 preceding changes.  This act makes punishment more severe for bullies and hopes to cut down on the bullying problems that seem to be plaguing our society.  However, this too has it’s own separate training and procedures, that take more time and energy away from planning and implementing lessons.  I believe that this is a valued change, and will eventually be as routine as training for sexual harassment, blood borne pathogens, and CPS reporting.  But starting it now, the timing just seems to stink.

6. Annual Professional Performance Review (APPR) – This has been a huge hot-topic for our state over the past year.  It encompasses the first 3 changes on this list, and then some.  I won’t even get too much into this one because it’s so up-in-the-air and no one (anywhere) can seem to figure out what is expected of us at the state level, nor agree on how this should be set-up.

Like I said, all of these are theoretically important and necessary changes to the education process.  Theoretically, they will make us greater teachers, and therefore our students will benefit more from that.  However, because all these changes are happening at the same time, they’ll be lucky if there are any teachers left in New York State crazy enough to pull it off.

Do you remember when you were a kid and you thought it was strange to see your teacher outside of school because you just didn’t picture them having a life outside of school?  Now it will be even more rare an occasion.

Bingo Review Game

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This week, I had 2 students in my room that needed to review for a Living Environment Evolution test.  I got a list of questions (with answers) from their teacher, and was told they were using them in a review game for the class.  Well, since I just had the 2 of them, I modified my review.  I told them to each make bingo boards with the answers of the questions.  There were 24 questions, and we made 5 by 5 squares with a free space in the middle.  They spent time writing in the answers anywhere on their board.  When they were done, I read off the question and they had to mark the answer on their board.  Now, since this was review, I had them tell me what they thought the answer was, so that they weren’t studying the wrong one.  I corrected them immediately (if needed) and continued with the next question.  They were allowed to switch their marker to the correct answer, but if I do this again next time, I may penalize them in some way so that they cannot just mark the right answer after getting it wrong.  Possibly, by marking incorrect answers with another color chip so that the space is dead and they need to make bingo in another way.  This will encourage students to make more educated guesses on their bingo answers.  I think this could work very well in any content area, and with any size group of people.

Always, Sometimes, Never

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I used this Thoughtful Education strategy today with my Algebra I student.  I’ve attached the worksheet I used (ASN Graphing Equations and Inequalities).  I used this strategy as a refresher, since my student is going into the next chapter, and can always benefit from connecting topic areas.  I knew that she was absent a lot during the lessons on graphing inequalities, so I made up this worksheet for her to complete.  When I made up the statements to put on the page, I thought of all of the important things that she will need to remember from the previous chapter to take with her into the current chapter.  Her evaluation of these statements gave me a better idea of what she still needed to revisit.

First of all, she said something that told me she didn’t know what an inequality was.  Because I was having a discussion with her, instead of just giving her busy work, I was able to pick up on this and correct it right away.  Once she knew what an inequality was (a statement using < or > or “less than or equal to” or “greater than or equal to”), she was able to work through the statements on her own, and then we reviewed them together.  During our discussion, it was clear she was solid on many of the aspects of graphing, but when it came to the shading statement, I realized she didn’t know how to actually graph an inequality, and that we needed more time to practice and review that.

I will definitely use this tool again, both as a pre-teaching tool and a reviewing tool.  Both will help me to know what they have learned correctly, and what we still need to focus on.  In a larger group setting, this will be helpful to know who really understands a certain topic, and who is skating through.

Active Learners for the Future

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I am a firm believer that students need to be actively engaged to learn.  The best teachers, and by far the most memorable lessons, incorporate active involvement in the classroom.  My favorite math teacher in high school taught us about locus points by taking us outside and rearranging us as locus points, situating us around stationary objects such as trees and sidewalks.  My second favorite math teacher taught us pre-calculus by encouraging us to explore various graphs to come up with rules for graphing them, and provided limited guidance in this process.  It was maddening, but I better learned how various types of graphs match up with their equations.

Nay-sayers to this method of teaching claim that teachers are being lazy, making the students do all the work.  I believe it’s quite the contrary.  Teachers have to take a lot of time and effort to plan a lesson that students will run themselves.  Teachers have to anticipate every direction that the lesson may go in.  Teachers have to remain astute to the conversations and actions around the classroom as an active lesson is being implemented, to make sure the students are staying focused to the task at hand.  People that oppose this method may also claim that with time constraints, material needs to be covered before state tests, and that active learning takes more time to implement.  While that may be true, wouldn’t it be better to have students learn the content better than try to race through content only touching on brief aspects?  Wouldn’t you get more out of your students with active learning because students would want to come to class and to stay attentive while there?

The alternative to active learning creates passive learners.  These are the types of learners that sit in class soaking up knowledge, just to squeeze it back onto an assessment and maybe, if they are lucky, to retain it.  These are the learners that never truly learn how to learn, or to do anything independently.  When they leave high school, they are lost in a sea of other passive learners, and do not know how to actively solve problems, or even how to find problems to solve.  When we create passive learners, we are setting them up for failure.

I believe that it is active learning that inspires students to continue learning.  I believe that it is active learning that causes students to continue to ask questions, and creates a spark for their passion of wanting to know more.  Active learners possess intrinsic motivation, the highest and most effective means of motivation, and the hardest for a teacher to cultivate.  However, once an active learner has been created, they are unstoppable, always looking for the answers to life’s questions, and always coming up with new questions to ask.  Why would we not want to have active learners in our society, in our future, and more importantly, in our classrooms?

Purpose of Preps

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To the untrained eye, prep periods may be seen as “free time” in the world of teaching.  Let me inform you of some of the uses of prep periods, keeping in mind that they are usually only 30-40 minutes in length, and it takes at least 5 minutes of travel time to and from your classroom to anywhere else in the building (office, bathroom, other teachers’ rooms, etc.).

  • going to the bathroom – important when trying to avoid UTI or other lady issues
  • making copies – because students (and others) tend to lose things
  • waiting for the copier – you’re not the only one with a prep and there are only 2 copiers in the building, if they’re working that day
  • Filling out paperwork – for the business office, or main office, or student referrals, etc.
  • grading papers, as well as calculating grades
  • connecting with other teachers (collaborating) – some issues are more pressing and cannot wait until the end of the day to discuss (i.e. “How did you want me to help Susie with her math when I see her next period?  What is she struggling with?”)
  • reading your e-mail – some issues are more pressing and cannot wait until the end of the day to discuss (i.e. “Susie and Sally want to fight today-watch out!”)
  • lesson planning – we all have lives outside of school (wait, that wasn’t a secret, was it?), and sometimes can’t stay until 5:30 preparing for the next day
  • calling home – Parents are just as much a factor in the equation of student success
  • exploring new ways to teach better – the internet is a wealth of knowledge, and like I said, we can’t always stay until 5:30 to get things done
  • running personal errands, like going to the bank, which on most days is not open by the time you would ordinarily leave school
  • peace of mind – let’s be honest, if we were with our students for every minute they were in school, we would all go crazy.  Even the best of teachers need a break from their students to recharge their minds, and to remind them why they love coming to work every day.  Give us a chance to miss our students!

Feel free to add your favorite prep time activity – something that you cannot live without during your 30-40 minutes of  “freedom”.