How I Would Fix Math Education

Posted on October 25, 2012 by mcashing

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.

The Elephant in the Room is sitting on my chest…

Posted on April 19, 2012 by mcashing

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.

More than I can chew, swallow, and digest properly…

Posted on April 6, 2011 by mcashing

I’ve always had a problem figuring out the breaking point of my to-do list. I seem to thrive when every second of my day is planned working on some project or another, even to the point that I almost feel guilty taking some time for myself to relax.

The same can be said for my new position. Sure, I was optimistic – I’m a Bill’s fan, I’m built that way. Sure, I can take on the behavioral kids that need a break from every-day classroom life. Sure, I can help to teach this kid math – after all, that’s what I’m certified in. Sure, I can help this kid pass the regents in January, no problem (even though I haven’t even looked at that Regents since I took it). Sure, I can take on this kid’s problems, and this kid’s problems, and so on and so on. ….wait. You want me to teach what that period? But I’m already teaching 2 other subjects that period, and only one of the 3 is something I’m certified in. But what choice do I have? I’ve already said yes so many times, how can I possibly start saying no?

I looked up a past post to see what I thought of all of this back in September, when I allowed myself time for reflection and contemplation, and before I got too dizzy to see straight:

“The ALC will temporarily house students that have had behavioral issues in the school, but this center will be a working classroom. Students will receive academic support for class assignments that need to be done. In turn, teachers who recommend a student to attend the ALC will provide appropriate assignments for those students to work on while at the ALC. Students will also receive behavioral support in the forms of Conflict Resolution and Character Education. Hopefully, this will take a more proactive approach and help the students to own their learning experiences and academic future.” – written on Sept. 9, 2010

The reality of the situation that I have let slowly spiral out of control is that I do not have time to focus on Conflict Resolution and Character Education with my behavioral students. I cannot fully meet their needs by giving them the attention they’re craving, and what most likely got them in my room in the first place. But they aren’t the only students this system is cheating. My instructional students are not getting my full attention. Even if I had no behavioral students assigned to me on any given day, there are 2 periods in which I am teaching 3 different subjects each. Five of these 6 subjects I give grades for. How is that fair to any of these students, who were each assigned to me with the idea that I would be able to give them individualized attention.

I have found myself in a hole that I helped create, and that I don’t even know when it got so deep.

This post is not my cry for help. This post is not my way of blaming anyone for how things got this way. This post is merely my way of thinking through the situation. Of course if anyone has any suggestions or comments, please let me know and I will put them into consideration. I just ask please for no “I told you so”s. I already know.

Homework in the Context of the New Family – Ch. 2

Posted on February 28, 2011 by mcashing

This chapter focuses on the varying differences of parent values and teacher values. Parents can range from the belief of “more homework is always better” to “there are better things than more homework.” Teachers need to be aware of these varying views, and be respectful of the wishes of the parents. At the same time, it is impossible to please everyone.

Gone are the days in which everyone in the community shared the same values, making things predictable. Now, people need to fear the legal ramifications of holding students to a moral standard that may not align with how the students were raised.

One example of differing priorities that is present on pages 32 and 33 reminds me of several students in Franklinville. They are responsible for helping out at home after school. When a school district mandated after school time to improve student grades, something that is similar to what we do, one parent complained of having to pay for a babysitter. As we continue to explore ways to help failing students, we need to keep in mind the parents’ values.

Since it is impossible for a school to demand homework on families, some teachers have found ways to be flexible: assigning work weekly or monthly, or even handing out a course syllabus (p. 34).

The variety of parents starts with parents who think helping their children with homework is not in their job description. At the other end of the spectrum we have parents that do their child’s homework to ensure good grades. As teachers, we need to be more aware of the level of difficulty for each student. The ideal, obviously, would be work that students could do on their own, without relying on the help of their parents.

On page 38, we see that homework is one of the leading causes of drop-outs. “The inability to keep up with homework was a critical factor in the decision of lower-class students to drop out of school.” The reality in Franklinville is that the majority of the demographic is of lower-class. There is little draw for a middle-class family to come to (and stay in) Franklinville. I believe that homework is a major factor for a few of our students who have dropped out, or are at risk for dropping out, even this year. I have been analyzing the Warning and Ineligible Lists for the year, and many of the names on there are people that have dropped out or that I am concerned for.

Parallel to the change in dictatorial parent relations, there was a change from dictatorial school relations. Schools and teachers used to be accepted as the experts on education, and parents saw schools as an institution that needed their support – simply because the school demanded it. Now, in a consumer-driven world, schools are viewed as a service that owes something to the parents, instead of the other way around. Schools that are in a lower tax-base area, and therefore do not have the funds to support themselves, no longer have the support of the parents as well.

This lack of volunteer involvement can be seen in other aspects of society as well. People no longer feel obligated ot help out at the local church, nursing home, library, or fire department. Instead, they are looking for involvement that can benefit themselves or their families. The only students involved in any kind of community service are either mandated by the court, or are seeking to bulk up their resume for college of National Honor Society.

On the other hand – in the minds of veteran teachers and administrators – supportive parents meant parents willing to do whatever a school said without question. Certainly those days are over. It may be perhaps that parents are more involved today than they used to be, simply because they are taking a stand as to what their child will or will not participate in during school.

So, how do we proceed? How do we close the gap between parent expectations and school expectations regarding involvement, especially with homework? The book gives a few suggestions on pages 46-54.

Get real – We cannot control every aspect of the child’s life.
Resist the temptation to judge – As we all know, whining will get you nowhere; accept what you’re given and welcome the support you do have. It’s easier to call students (and possibly their parents) lazy than to analyze our own teaching models.
Revise expectations of Parental Support – Schools shouldn’t expect all parents to be involved, yet subconsciously, we do.
Suggest (not mandate) guidelines for the parents’ role in homework – We (as a school district) need to be in constant communication with parents – letting them know what we expect from them at various grade levels. Parents need to be letting us know when an assignment is too difficult, or the students needed help with something. This way, when it returns completed, we don’t assume that the child understands the content. Wording these guidelines can be tricky, so some examples are given on p. 50 in Figure 2.1.
Establish formal methods of parent-teacher communication – There are a few surveys that are available on pages 51-53 that can serve as a tool for parents to communicate to the schools about homework views. The homework card (Figure 2.2) should be filled out for each individual student. The Parent Survey (Figure 2.3) would be easy enough to include in beginning of the year paperwork, and be made available to the teachers, so that the parents only have to fill out one each year instead of per child, save for question #1. There is also a Parent Feedback checklist (Figure 2.4) designed to go along with every assignment. I would send these out the first week that homework goes out, and then as different styles of homework go out throughout the year.
Set parents’ minds at ease about homework – Parents who have tried communicating with the school and feel that they are not being heard are weary of doing it again. They see talking to teachers about homework the same as talking to a wall. We need to collectively reassure them that their child will not be penalized for not completing homework that the students gave their best effort on.
Endorse a set of inalienable homework rights – There is an example of one such Bill of Homework Rights in Figure 2.5 on pg. 55.

We need to work together as a school district and community to figure out how best to handle homework for our students. It will require patience, respect, and effort from both sides.

The Cult(ure) of Homework – Ch. 1

Posted on February 16, 2011 by mcashing

Homework has been such an institution in our educational system, it may be difficult to even think of not having it. However, while our method of education has changed and evolved in the past 150 years, the concept of homework has changed very little.

In the early days of our educational system, one-room school houses were the norm, combining many grade-levels for one teacher, with attendance being even more sporadic than it is now. Assessment of knowledge consisted of students memorizing facts and reciting them back to the teacher. To better prepare for these assessments, students would study at home (hence, homework), (p. 3).

Since those early days in the late 1800s, assessment procedures have evolved to include projects, papers, and other more creative things. While these methods of assessment are better suited for the goals that we have for our students – encouraging higher cognitive activity – these methods are also time consuming.

Unfortunately, teachers have precious few hours of class time for instruction, let alone assessment. As a result, these time-consuming, elaborate projects get pushed on home time. Moreover, the projects often need the help of parents to make sure they are done, and done well. This begs the question: What are we assessing? Are we assessing how well the students know the material, or how well the parents can help them accomplish something elaborate and beautiful?

There are compelling arguments on either side of the “To (give) Homework or Not To (give) Homework” debate. For those in favor of homework, their arguments are in bold. The rebuttals to these arguments will be found directly following them. These bolded beliefs are straight from the book, and can be found on pages 10-13.

#1 – The role of the school is to extend learning beyond the classroom.

While it may be true that some students do not have the parental support teachers wish to see, does that make it the educator’s responsibility to make up for the supposed lack of parental support? Do we really want to control every aspect of our students’ lives, giving them no break from school? I don’t want to put words in my fellow teachers’ mouths, but if people demanded me not to have a break from school EVER, there may be a mutiny on our hands. Of course, most teachers are so passionate about teaching that they cannot get enough of it, and spend a lot of their free time researching to make their teaching more effective (such as, if you are bothering to read this right now). But, they CHOSE their profession for their passion. Students do not have the luxury of choosing their homework.

#2 – Intellectual activity is intrinsically more valuable than nonintellectual activity.

While I agree that intellectual activity is important to the growth of a child, I also believe that a child needs to be well-rounded. They need to grow socially, emotionally, and physically, as well as intellectually. They need more than just academics to survive as a citizen in this world, and we would be stunting them of this growth if we demanded that they only focused on the academic aspects of schools. After all, experienced teachers know that a child learns best by doing. It would then make sense that the best way for them to learn social skills is to participate in social events: play dates, unstructured play time, etc.

#3 – Homework teaches responsibility.

As they argue on page 11, when they say responsibility, they really mean obedience. We are not teaching responsibility in assigning an hour of homework a night, we are training them to be obedient. There are better ways to reinforce responsibility, that will be explored in future chapters.

#4 – Lots of homework is a sign of a rigorous curriculum.

In other words, the curriculum is so busy, we cannot possibly teach you everything you need to learn in the classroom, so you must have homework to continue the teaching at home. I believe homework should be a time for practice, not a time for instruction; but more on that later. This idea of more homework caters more to the parents than to the students. Most students see the homework involved with a class or teacher and the more there is, the harder they think the class is. Students figure this out in September, from the opening week expectations that teachers share. Some may even be so tuned in that they notice the year before, watching their older friends and their work load. “Oh, I don’t want Mrs. So-and-so. She gives a TON of homework!” Therefore, before they’ve even experienced it for themselves, students have a defeated attitude. For many of them, it’s a self-fulfilling prophecy.

#5 – Good teachers give homework, good students do their homework.

This statement sums up the other 4 statements. It is a mentality accepted by all; an unspoken truth. Non-tenured teachers think it is expected of them by administration, and often times fall into the trap of using homework to extend their instructional time. Parents have come to expect it because, after all, “that’s how we got through school.” Students are trained to think it, getting rewards for getting their homework done (good grades, stickers, tickets, etc.), and punished if they’ve forgotten it (bad grades, loss of free time, etc.).

On the whole, I don’t totally disagree with the idea of homework. I do believe that we can get tunnel-vision and lose sight of the true reasoning behind it. I believe homework should reinforce what has been already learned in the classroom. A very wise teacher once told me that she never assigns work that she wouldn’t be willing to do herself. This has helped to keep me in check over the years.

I write this as I am surrounded by students at an extra-curricular activity. Any down-time that the students have is devoted to rushing to complete their homework. I’ve heard a few offer to trade assignments with each other just to get it done. Students are smarter than we give them credit for, and they too can see there is no value in giving homework just to give homework.

Reflections on Rethinking Homework

Posted on February 16, 2011 by mcashing

I have currently started reading a book that I’ve had for some time now, and would like to document my ideas and thoughts about it on this site. The book is Rethinking Homework: Best Practices That Support Diverse Needs by Cathy Vatterott. I received this book from a colleague earlier this fall, and am finally creating time to read it and analyze it.

Since this is a borrowed book, I don’t want to write all over it, like I normally would. So, this is my outlet for organizing my thoughts. Plus, there is a committee of teachers at my school also reading this book. I would love to be able to share thoughts with them on it as well.

Please feel free to share your thoughts on homework, and to pick-up your own copy of the book (or borrow it from a friend) – it’s a very thought-provoking read.

A new look at Classroom Management

Posted on October 13, 2010 by mcashing

Yesterday, my school had the opportunity to listen to Brian Mendler speak. It was refreshing, to have a professional development speaker that moved around, and didn’t rely on his powerpoint, and didn’t read to us; that engaged us and made us feel valued, and motivated us. Well, me at least.

Something that students appreciate from teachers is their honesty. Brian Mendler showed us that yesterday. He honestly told us about real situations, his real story. He honestly told us about how teachers are perceived from students, and we all laughed – because it was true! And you could tell the nerves he was hitting by the people how were uncomfortably laughing versus people who were out-rightly laughing. He talked about teachers that were rigid and policies set in stone, and people who got caught in power struggles. And then he talked about strategies to do instead of the rigid ones that we all learned from our own teachers.

He talked about empowering the students. Students rarely get a chance to have power, but they will try to get it whether you give it to them or not. They can either fight for it, or you can give it to them. And it doesn’t have to be an “I give up” form of teaching (which I’ve also seen in classrooms). It’s giving students power in a constructive way. Let them omit a question on the test and replace it with one that they really know the answer to. Let them ham it up in front of the class for 3 minutes to start the ball rolling (instead of them hamming it up during your lesson). Talk with them individually – it doesn’t have to be a conversation, you could be giving them positive (or negative) feedback in their ear for only them to hear. But, make sure you equally give positive feedback to cancel out the negative.

He talked about keeping the kids in the classroom as long as possible. Now there are some veteran teachers that cringe at this. But let me explain why it’s important. Students know that if they bug you enough, you’ll kick them out of their class. It’s not a punishment for them if you kick them out of math. And when they inevitably come back, you’ve got an even bigger problem than you started with. They have all the power and they got it the wrong way. And you let them have it that way. So how do you diffuse the situation? Humor. So they call you names. You can take it, you’re the adult, remember? What do you tell your kids to do in a fight situation? Walk away. Try it. Let them have the last word. They need it to save face to their friends, and they will have the last word if it’s the last thing they do in your class.

He talked about Multiple Intelligences learning, indirectly – using the gym for teaching graphing, singing songs to learn content in any area, working in groups to work on inter- and intrapersonal personalities.

We shared strategies with each other, and practiced some of the ones he discussed: 4-2-1, group work with roles (leader, writer, presenter, etc.), music stands, green-yellow-red cups, carpet squares – the list goes on forever.

It was refreshing to get back to an idea of teaching because we’re passionate about it, not just because we have to. I don’t want to be the kind of teacher that counts down the days, months, and even years to retirement. And I don’t want my kids to have those kinds of teachers either.

Closed Properties

Posted on September 22, 2010 by mcashing

I just taught a class on closed properties (ex. the set of Natural Numbers is closed under addition). Unfortunately, not having a lot of time to plan, I just ran through the notes, and way over the kids’ heads. Upon further thought, I would’ve explained it like this:

A set of numbers is like a classroom. (this illustration works best for a finite set of numbers)

For example, I have a set {-1, 0, 1}. Pretend that the {} are little doors into the room. Now, we’re going to perform all the operations on these numbers. If we come up with an answer that is still in this room, the doors stayed CLOSED (we didn’t have to open them to find the solution).

Let’s try it:

Addition: -1 +1 = 0; -1+ -1 = -2 **-2 wasn’t already in the room, therefore we had to OPEN the door to let it in (not closed!)
Subtraction: 0 – -1 = 1; 1-1 = 0; -1 – -1 = 0; 1 – -1 = 2 **2 wasn’t already in the room, therefore we had to OPEN the door to let it in (not closed!)
Multiplication: 0 x 0 = 0; 1 x 1 = 1; -1 x -1 = 1; -1 x 0 = 0; 1 x 0 = 0; 1 x -1 = -1 ** because I tried every possible combination of numbers, and my solutions were always already in the room, my door stayed CLOSED
Division: 0 / 1 = 0; 1 / 0 = does not exist **this answer obviously isn’t in the room, therefore we had to OPEN the door to let it in (not closed!)

How to avoid egg on your face…

Posted on September 10, 2009 by mcashing

…when setting up your centers, actually try them out. This way, you know ahead of time that the head phones don’t work, and that you forgot to put out the bingo chips, and you have NO IDEA where the timer went from packing it away last year! This way, you also avoid using all your center time preparing these things, and you can actually let the kids work independently.

…ask when you don’t know something! I found out today that our textbooks for ELA and Math have extensive teacher resources on their websites, and since all of our classrooms are lucky enough to have projectors in them, we can use them a lot! Wow, so wish I knew that before! Plus, now that I can access those websites, I can work on my plans at home without lugging the huge teacher edition books home with me! All on-line, I love technology!

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